Long Term Degradation of Resin
for High Temperature Composites
by
Kaustubh A. Patekar
B.Tech., Aerospace Engineering (1995)
Indian Institute of Technology, Bombay, India
Submitted to the Department of Aeronautics and Astronautics
in partial fulfillment of
the requirements for the degree of
Master of Science
in Aeronautics and Astronautics
at the
Massachusetts Institute of Technology
September 1998
© Massachusetts Institute of Technology 1998
All rights reserved
Signature of Author
Department of Aeronautics and Astronautics
June 19, 1998
Certified by
Hugh L. McManus
Associate Professor of Aeronautics and Astronautics
Thesis Supervisor
Accepted by
S ~47ii Professor
Peraire
Associate
Chairman, Department Graduate Committee
INSTIThTE
MASSACHUSETrS
MASSACHUSETTS INSTITUTE
I
OF TECHNOLOGY
SEP 2 2 1998
LIBRARIES
1
LONG TERM DEGRADATION OF RESIN FOR HIGH
TEMPERATURE COMPOSITES
by
Kaustubh A. Patekar
Submitted to the Department of Aeronautics and Astronautics on June 19, 1998 in partial
fulfillment of the requirements for the Degree of Master of Science in Aeronautics and
Astronautics
ABSTRACT
The durability of polymer matrix composites exposed to harsh
environments is a major concern. Surface degradation and damage are
observed in polyimide composites used in air at 125-300'C. It is believed that
diffusion of oxygen into the material and oxidative chemical reactions in the
matrix are responsible. Previous work has characterized and modeled
diffusion behavior, and thermogravimetric analyses (TGAs) have been carried
out in nitrogen, air, and oxygen to provide quantitative information on
thermal and oxidative reactions. However, the model developed using these
data was not able to capture behavior seen in isothermal tests, especially
those of long duration. A test program that focuses on lower temperatures
and makes use of isothermal tests was undertaken to achieve a better
understanding of the degradation reactions under use conditions. A new,
low-cost technique was developed to collect chemical degradation data for
isothermal tests lasting over 200 hours in the temperature range 125-300'C.
Results indicate complex behavior not captured by the previous TGA tests,
including the presence of weight-adding reactions. Weight gain reactions
dominated in the 125-225oC temperature range, while weight loss reactions
dominated beyond 225 0 C. The data obtained from isothermal tests was used
to develop a new model of the material behavior. This model was able to fully
capture the behavior seen in the tests up to 275°C. Correlation of the current
model with both isothermal data at 300 0 C and high rate TGA test data is
mediocre. At 300'C and above, the reaction mechanisms appear to change.
Attempts (which failed) to measure non-oxidative degradation indicate that
oxidative reactions dominate the degradation at low temperatures. Based on
this work, long term isothermal testing in an oxidative atmosphere is
recommended for studying the degradation behavior of this class of materials.
Thesis Supervisor:
Title:
Hugh L. McManus
Associate Professor
Department of Aeronautics and Astronautics
Massachusetts Institute of Technology
ACKNOWLEDGMENTS
A number of people contributed in various ways towards this endeavor.
First of all, I would like to thank Hugh, my advisor, for his guidance and
encouragement. I have enjoyed working for him. The discussions I had with
him helped form the basis of this work and his suggestions were
instrumental in making my life a lot easier.
I would also like to thank Paul, Mark, Carlos and Prof. Dugundji for
their comments and questions during TELAC presentations. The discussion
on issues raised during these talks helped to improve the quality of this work.
John Kane's help in getting my long-lasting tests done is greatly appreciated.
Deb, thank you for keeping me company while waiting for Hugh and
enduring my " Where is Hugh ?" questions, especially during the last two
months. Thanks Ping for decoding all those requisition forms. Thanks are
due to my UROPers Jeff Reichbach and Ryan Peoples, for going through
numerous catalogs and building the experimental set-up.
I owe a lot to other grad students in the lab, who have made this time
fly by. Chris, for keeping me company while working at ungodly hours in the
office (I have never seen him leave for the day). Tom, for being nice and
letting me use the thermal chamber for a really long time. Lauren, Brian
and Dennis for all those chats, which were good, relaxing breaks. All those
who have offices in 41-219, for sharing the joy of working in a place that
continues to oscillate between the equator and Antarctica.
Last, but not the least, I would like to thank my parents and brother,
Shailesh, for their continued support and encouragement.
FOREWORD
This work was conducted in the Technology Laboratory for
Advanced Composites (TELAC) in the Department of Aeronautics and
Astronautics at the Massachusetts Institute of Technology.
This work was supervised by Dr. K. J. Bowles of the NASA
Lewis Research Center and was carried out under Grant NAG3-2054,
"Improved Mechanism-Based Life Prediction Models."
TABLE OF CONTENTS
LIST OF FIGURES
7
LIST OF TABLES
8
NOMENCLATURE
9
1. INTRODUCTION
10
2. BACKGROUND
15
2.1
PREVIOUS EXPERIMENTAL STUDIES
16
2.2
POLYIMIDE CHEMISTRY
19
2.3
PREVIOUS ANALYTICAL WORK
22
2.4
RECENT WORK
24
3. PROBLEM STATEMENT AND APPROACH
28
3.1
PROBLEM STATEMENT
28
3.2
APPROACH
28
3.3
ANALYTICAL TASKS
29
3.4
EXPERIMENTAL TASKS
29
4. ANALYTICAL METHODS
31
4.1
DEGRADATION MODEL
31
4.2
DETERMINATION OF KINETIC CONSTANTS
35
4.3
MODEL IMPLEMENTATION
36
4.4
DATA REDUCTION IMPLEMENTATION
36
5. EXPERIMENTAL PROCEDURES
39
5.1
MATERIAL MANUFACTURE AND PREPARATION
40
5.2
EXPERIMENTAL PROCEDURE FOR ISOTHERMAL
42
TESTS
5.2.1
Experimental Set-up
42
5.2.2
Tests in Air
43
5.2.3
Tests in Nitrogen
46
6. RESULTS AND DISCUSSION
48
6.1
6.2
LONG TERM ISOTHERMAL AGING TESTS IN AIR
48
6.1.1
Experimental Data
48
6.1.2
Data Reduction and Correlation
58
LONG TERM ISOTHERMAL AGING TESTS IN
68
NITROGEN
6.3
7.
COMBINED MODEL
72
77
CONCLUSIONS
79
REFERENCES
APPENDIX A
MATLAB CODES
85
APPENDIX B
ISOTHERMAL AGING IN AIR TEST DATA
96
LIST OF FIGURES
1.1
Complete analysis for composite degradation
12
5.1
Schematic of specimen and thermocouple location in thermal
environment chamber (not to scale)
44
5.2
Schematic of atmosphere control system for aging tests in inert
atmosphere
47
6.1
Isothermal aging test in air at 125°C
50
6.2
Isothermal aging test in air at 150'C
51
6.3
Isothermal aging test in air at 175°C
52
6.4
Isothermal aging test in air at 200°C
53
6.5
Isothermal aging test in air at 225°C
54
6.6
Isothermal aging test in air at 250°C
55
6.7
Isothermal aging test in air at 275°C
56
6.8
Isothermal aging test in air at 300'C
57
6.9
Model comparison with isothermal aging test data in air at 150'C
61
6.10
Model comparison with isothermal aging test data in air at 175°C
62
6.11
Model comparison with isothermal aging test data in air at 200°C
63
6.12
Model comparison with isothermal aging test data in air at 225°C
64
6.13
Model comparison with isothermal aging test data in air at 250'C
65
6.14
Model comparison with isothermal aging test data in air at 275C
66
6.15
Model comparison with isothermal aging test data in air at 300°C
67
6.16
Isothermal aging test in nitrogen at 125°C
69
6.17
Isothermal aging test in nitrogen at 200°C
70
6.18
Isothermal aging test in nitrogen at 300°C
6.19
Comparison of combined model prediction with 5C/min.
heating rate TGA data in air
Comparison of combined model prediction with 20C/min.
heating rate TGA data in air
71
74
6.20
75
LIST OF TABLES
5.1
Neat resin isothermal exposure test matrix
41
6.1
Coefficients for the new three reaction model
60
6.2
Coefficients for the combined five reaction model
73
B.1
Data for test at 125 0 C
96
B.2
Data for test at 150 0 C
97
B.3
Data for test at 175 0 C
98
B.4
Data for test at 200 0 C
99
B.5
Data for test at 225 0 C
101
B.6
Data for test at 250 0 C
102
B.7
Data for test at 275 0 C
104
B.8
Data for test at 300 0 C
105
NOMENCLATURE
cox
cs
Ci
E,
Eij
F'(T)
F(ai)
k;
kj
mf
mi
mij
mo
msi
mfi
moi
ni
nij
Mo
M(t)
R
t
T
V
Yi
ai
ai,
Am
Am
Am'
Ami
AM
relative concentration of oxygen
relative concentration of species s
constant used for modeling reaction during data reduction
activation energy of reaction acting on component i
activation energy of reactionj acting on component i
temperature-dependence function
conversion-dependence function for component i
rate constant for reaction acting on component i
rate constant for reactionj acting on component i
final mass of unreacting mass fractions
mass lost due to completion of reactions on component i
concentration-dependency of reactionj acting on component i
original mass of material in an infinitesimal control volume
concentration-dependency of reaction acting on species s
final mass of component i
original mass of component i
order of reaction acting on component i
order of reaction i acting on component i
original sample mass for experiments
sample mass measured at time t
real gas constant
time
absolute temperature
specimen volume
mass fraction of component i
mass loss metric for component i
mass loss metric for reactionj acting on component i
total mass lost from control volume
normalized mass loss for sample used in tests
normalized mass lost from control volume
mass lost from component i
total mass lost from volume V
CHAPTER 1
INTRODUCTION
Polymer matrix composites are being increasingly used in applications
where they are exposed to harsh environmental conditions such as high
temperatures, thermal cycling, moisture, gases, oils and solvents. Exposure
to such environments leads to degradation of composite materials, potentially
affecting the structural integrity and useful lifetimes of composite structures.
Some of the well-known aerospace applications of polymer matrix composites
(PMCs) include engine supports and cowlings, reusable launch vehicle parts,
radomes, thrust-vectoring flaps and thermal insulation of rocket motors.
The increasing demand for such applications has led to extensive
efforts for the development of materials which have upper use temperatures
in excess of 150'C. These materials should be able to withstand a wide range
of temperatures without significant reduction in their mechanical properties,
be chemically resistant to the environment and exhibit low mass loss at
extended aging times at their upper use temperatures.
The behavior of PMCs exposed to high temperatures for extended
durations is not well understood. A variety of effects are observed on matrix
materials, including specimen mass loss, specimen shrinkage, the
development of a severely degraded surface layer, formation of voids, the
development of surface microcracks, and the degradation of mechanical
properties. The problem is further complicated by the anistropic nature of
composite materials. The fiber/matrix interface provides additional sites for
10
both degradation and the formation of cracks.
Composite laminates also
experience thermally (or mechanically) induced interply microcracks in the
matrix material.
These cracks can then provide new pathways into the
interior of the material for the external environment, resulting in more
severe degradation of the laminate as a whole.
The interaction of these
effects during the aging period results in a highly complex, coupled problem
where the identification of individual mechanisms and their contributions
becomes extremely difficult.
As noted by Cunningham [1], design of high temperature structures
would be greatly improved through the development of a model which could
incorporate known quantities such as laminate geometry, material
properties, temperatures and chemical environment, and from these
determine quantities such as the material degradation state as functions of
exposure time and position within the material. A schematic of the desired
coupled analysis which could provide this capacity is shown in Figure 1.1.
The analysis consists of several individual modules which address different
aspects of the problem.
Inputs to the model include the exposure
environment and the applied mechanical loads.
For a comprehensive
analysis, it is necessary to calculate the thermal response, diffusion and
chemical degradation state, and the thermo-mechanical response of the
system. The thermal analysis supplies the diffusion and reaction chemistry
model with the necessary temperatures. This module can then provide the
thermo-mechanical analysis with predictions of the chemical state within the
material.
Results from these analyses can then be used to determine
whether damage (and ultimately failure) occurs. The effects of damage on
material properties, thermal response and the reaction chemistry is
accounted for in an incremental fashion, allowing a truly coupled
11
Figure 1.1
Complete analysis for composite degradation
representation of the problem. Though substantial success has been achieved
in solving different sections of this complex problem, the chemical
degradation has not been adequately quantified.
The current research uses, and hopes to validate, a mass loss (or gain)
metric for the chemical degradation within a polymer matrix composite
material. The extent to which such a metric can be used for developing
predictive capability, assuming that the time and nature of environmental
exposure of a composite are known, is studied. The approach found to be
useful by other researchers [1],[2] consists of using Arrhenius reaction
kinetics to model chemical reactions which occur within the material. Two
types of reactions are considered: thermal reactions which depend primarily
on the duration and temperature of exposure, and oxidative reactions which
also take into account the exposure to oxygen.
The goal of the current research is to establish an analytical
methodology which can be used to predict the degradation states at all points
within a composite laminate as functions of exposure time and environment.
The analysis uses Arrhenius reaction kinetics to model the chemical reactions
which occur within the material.
Multiple, simultaneously occurring
chemical reactions, including both purely thermal reactions and reactions
that depend on diffusing substances, are taken into account. Some of the
earlier work, which formed the basis for this work, showed that the
concentration of diffusing oxygen controls some of the chemical reactions. In
this work we studied only powdered matrix materials so as to decouple the
diffusion effects from
the chemical effects.
A better understanding is
currently needed of these chemical effects.
Experimental studies were carried out to characterize the nature of
chemical reactions, and to determine appropriate models and to quantify
13
them with kinetic reaction coefficients.
Long term isothermal tests for
duration in excess of 200 hours were carried out on finely ground neat resin
powders in both thermal and oxidative environments.
The use of fine
powders, which have very large surface area to volume ratios, effectively
eliminates the diffusion effects which can be seen in finite-sized specimens
[3].
Mass losses were measured for tests carried out at different
temperatures and this data was used to obtain the required chemical reaction
coefficients for the model.
Some of the earlier work had utilized thermogravimetric analyses
(TGAs)
samples.
for measuring the mass loss and mass loss rate on powdered
However, this technique was found to be very expensive for
conducting long term isothermal tests. A new cost-effective technique was
developed for conducting these tests. This technique makes use of an oven
with a temperature controller, a custom setup for holding the sample, and a
sensitive weighing balance to measure the sample mass periodically.
Previous work relevant to the current research and some of the
research which led to this work are described in Chapter 2. This includes
analytical and experimental studies on the degradation of high temperature
PMCs as well as a background on the analytical chemistry used in the course
of this work. The problem statement and approach for the current research
is presented in Chapter 3.
Chapter 4.
The analytical methodology is developed in
Chapter 5 describes the experimental procedure that was
developed to collect data for predicting required material coefficients.
Experimental results, as well as correlation between experimental data and
model predictions is presented and discussed in Chapter 6.
Finally,
conclusions reached on the basis of this work are presented in Chapter 7.
14
CHAPTER 2
BACKGROUND
A number of polymer matrix composites are being used in the
aerospace industry for high temperature applications.
Most of these
materials are thermosetting resins which can be chemically classified as
bismaleimides and polyimides. These resins have proven to be better than
traditional polymer systems in terms of chemical resistance, ability to
withstand high temperatures, and maintaining structural strength and
integrity. However, documenting the behavior of these materials has clearly
shown that these materials degrade with continued exposure to high
temperatures.
The durability issues related to these materials need to be
well understood in order to use them with confidence in primary structure
applications and to improve the design of aerospace components where they
are currently being used.
Introduced in the early 1970s by researchers at NASA Lewis Research
Center, PMR-15 and other polyimides are among the most widely used in
high temperature applications.
These materials exhibit the required
mechanical properties and thermo-oxidative stability [4], [5], [6].
While
PMR-15 has been used in continuous service at 500 to 550F, some of the nextgeneration materials withstand continuous service of 600 to 700F with
excursions to 800F and beyond.
Most of the experimental work carried out to improve the
understanding of these materials has focused on the collection of
experimental data, with the idea of creating a database of the effects of
15
extended exposure to high temperatures. Some of the recent work has tried
to build empirical modes for correlating the degradation effects with changes
in material properties such as strength and weight. There is only a small
amount of work which has tried to quantify the phenomena with the aim of
building accurate analytical models.
Most of the analytical work has led to the building of case-specific
quantitative models and only a very limited number of mechanism-based
models [1], [7]. These mechanism-based models were successful in capturing
some of the degradation phenomena.
However more work is needed for
developing predictive capability based on these mechanism-based high
temperature degradation models.
Some of the relevant experimental studies and analytical work is
reviewed in this chapter. Studies in the area of polymer chemistry are
discussed in order to give adequate background for this work, which focuses
on quantifying the reaction mechanisms.
2.1
PREVIOUS EXPERIMENTAL STUDIES
The extensive experimental data on high temperature degradation can
be broadly classified into three categories - effects of aging on neat resin [8],
[9], bare fibers [10], [11], [12], [13] and composite materials [4], [14], [15],
[16].
Mass loss, shrinkage, and changes in thermal, mechanical and
viscoelastic behavior have been reported. Limited correlation exists between
individual studies.
A study by Bowles [9] on the effects of aging on neat PMR-15 resin
revealed that several coupled mechanisms proceed simultaneously in the
early stages of degradation at elevated temperatures in air. Samples exposed
for up to 3000 hours at temperatures ranging between 288 0 C and 343°C
16
exhibited mass loss, specimen shrinkage, the formation of a distinct surface
layer, development of surface microcracks, and the degradation of mechanical
properties. Mass loss occurs throughout the duration of the aging periods
observed, and in the presence of oxygen results in the formation of a
distinctive thin layer on the exposed surfaces of the polymer. Voids develop
within the surface layer and increase in size and density over time, acting as
starter points for cracks which grow from the exposed surfaces.
The
similarity between the observed surface layer growth rates and mass loss
rates suggests that degradation-induced mass loss primarily occurs within
this thin surface layer, while the core of the material is relatively protected
from oxidative degradation. This suggests that diffusion of environment into
the material plays a key role and is coupled with the chemical degradation
phenomenon.
Similar investigations on the effects of aging at elevated temperatures
on bare fibers have also been conducted.
Bowles [12] found that extended
exposure in air resulted in mass loss from graphite fibers. Data from this
study suggested that carbon fibers such as Celion 6000 consist of a layered
microstructure which has a relatively non-porous outer skin surrounding a
porous core. As the outer layer degrades the environment gains access to the
inner, porous core, resulting in an acceleration of the degradation process.
This effect was also noted by Wong et al. [13] in a study on the thermooxidative stability of IM6 fibers in air. In contrast, fibers in composites are
protected - virtually no surface area is exposed to the environment and no
mass loss is observed [11]. This suggests that adequate quantification of the
matrix degradation is important for studying composite behavior at high
temperatures as the fibers will not be exposed to environment in most cases
where such materials are used.
Unidirectional
demonstrate
composites
similar
degradation
mechanisms to neat resin, although the mass loss is less severe. Mass loss
appears to be dependent on the matrix volume fraction [14], suggesting that
preferential degradation of the matrix takes place. A study on the effects of
different aging environments on the mass loss from unidirectional graphitefiber/PMR-15 composites recorded significant differences in the mass loss
behavior in inert and oxidative atmospheres [4].
Mass losses in inert
atmospheres asymptotically approached stable values over a period of time at
each of the test temperatures. The majority of the mass loss occurs within
the first few hundred hours of aging and appears to be a bulk mechanism,
depending only on specimen volume. After the first 150 hours of aging, mass
losses from the specimens at each of the aging temperatures have essentially
reached their final values, which increases with exposure temperature. This
behavior suggests that only the initial portion of the mass loss curves reflect
thermally activated processes. In contrast, specimens exposed to oxidative
atmospheres will continually lose mass over the entire aging period. Notably
higher mass loss rates are demonstrated in air than in an inert atmosphere
at the same temperature. Aging in oxidative atmospheres always results in
the formation of degraded surface layers.
As aging time is increased, a
distinct layer of degraded matrix forms at the surfaces and advances into the
composite [15]. This layer growth is similar to that observed in neat resin [9].
Scola and Vontell [16] measured the flexural and shear properties of graphite
fiber/PMR-15 composites, isothermally aged at 316 0 C for periods up to 2000
hours, for a number of different fibers. SEM analysis of fractured surfaces
was carried out and optical micrographs of cross-sections were taken. They
observed that composites with high initial shear strength exhibited the
greatest resistance to reduction in shear strength. They did not hypothesize
18
the possible cause of this behavior. These data seem to suggest that the
fiber/matrix interaction played a role in the degradation of the composite
shear strength.
The influence of the fiber reinforcements on thermo-oxidative stability
has been addressed by several research efforts [10], [11], [14] in trying to
explain the accelerating effect of exposed graphite fiber ends on mass loss
rates in composites.
These researchers recorded different behavior in
composite materials with different fiber reinforcements.
The mass loss
behavior was blamed on the effects of impurities in fibers; which in turn
allowed fiber degradation, exposing greater matrix surface are to
degradation. The most thermally stable fibers do not necessarily result in
the most stable composites, and in some cases result in the least thermooxidatively stable configurations [12].
2.2
POLYIMIDE CHEMISTRY
The degradation behavior which has been observed empirically is
dependent primarily upon the chemistry of the matrix material. The PMR-15
material considered in the course of this work is chemically quite complex.
PMR polyimides are addition-type thermosetting polymers prepared by the
polymerization of monomer reactants (PMR). Resin solutions consist of three
individual monomers - a nadic ester (NE), the dimethyl ester of 3,3',4,4'benzophenotetracarboxylic acid (BTDE), and 4,4'-methylenedianiline (MDA)
dissolved in methanol.
When these monomers are combined in a
2.000/2.087/3.087 molar ratio respectively, the formulated weight after
imidization, but before crosslinking, is 1500. Resin of this composition is
designated PMR-15 [17] . The chemistry of the formation of this building
block is quite well understood [18] , however the chemistry involved in the
19
polymerization and later cross-linking of the material is still subject to much
debate with no definitive answer as yet available [8], [19].
The chemistry
involved in the degradation of this and other related systems is under
investigation but it is not yet understood to a level which would allow definite
conclusions to be drawn and predictive calculations to be made.
Evidence suggests that cross-linking within the material is not
complete at the end of the post-cure period, and hence one aspect of the aging
process is the completion of cross-linking reactions. Studies have linked this
increase in cross-link density within the material to the initial increase in
material properties such as the glass transition temperature and compressive
modulus [2], [20].
The fully cross-linked material is subject to both oxidative attack and
thermal degradation at a variety of sites, both in the cross-links and in the
main polymer chain itself at a variety of vulnerable links [21]. The mass loss
over extended aging times is attributed to the degradation of the nadic ester
and MDA components of the main polymer chain while the BTDE component
remains relatively unaffected [22]. The nadic ester appears to be the most
vulnerable to oxidative attack and is thus the weak link in the thermooxidative stability of these materials, with an increase in the nadic ester
content in the PMR formulation resulting in a decrease in the thermooxidative stability of the compound [23]. PMR formulations using the MDA
component demonstrated lower mass loss and higher material property
retention than PMRs formulated using more a stable monomer in place of
MDA. This effect has been attributed to a synergy between the MDA/NE
components which provides sites vulnerable to oxidation in the PMR polymer
chain.
These sites promote weight-gaining reactions (such as carbonyl
formation and thermo-oxidative cross-linking) in surfaces exposed to air,
20
resulting in the polymer possessing a higher thermo-oxidative stability as a
whole [21].
PMR-II-50, also developed at NASA is formulated with a hexafluorodianhydride (the diester thereof, 6FDE) instead of BTDE, for increased
thermo-oxidative
stability in the prepolymer
backbone, and para-
phenylenediamine (PPDA), replacing MDA. Prepolymer molecular weight is
higher at 5000. This results in a 50 to 100F increase in the thermal stability,
with some sacrifice in glass transition temperature due to cross-linking [5].
A great deal of mechanistic information concerning polyimidie
degradation has been ascertained from analysis of the degradation products,
both volatile off-gases and solid residues.
The most prevalent products
evolved during thermolysis of a polyimide are CO2, CO and H20.
At
temperatures below about 350 0 C, C02 is the predominant gaseous byproduct. Above 350 0 C, CO evolution commences and becomes pre-dominant
above 4000 C. The compositions of the volatile degradation products produced
in air and nitrogen are qualitatively similar although rates of their formation
are much greater in air [24].
Releases of larger fragments of the polymer
may follow. In an inert atmosphere such as nitrogen, approximately 60% of
the initial mass of the polymer will remain as char up to 800 0 C. In air, the
more aggressive nature of the environment results in all of the mass being
eventually consumed at these temperatures [25].
While the basic theory
behind the chemistry of this degradation behavior is currently receiving
considerable attention, the efforts in this area to develop a more complete
understanding of this phenomenon remain too diverse to allow the
development of a definitive model of the mechanisms which occur. A more
focused research effort is required for achieving this goal.
2.3
PREVIOUS ANALYTICAL WORK
The confounded nature of experimental data due to the coupling of
various physical effects, and the complex nature of PMR-15 chemistry,
suggest the use of semi-empirical methods for modeling the degradation
behavior. Various physical effects (e.g. diffusion vs. chemical reactions) can
be studied by planning a careful set of experiments that decouple the physical
effects.
The chemistry has proven more difficult.
Reasonable modeling
success could be achieved, without a complete understanding of the
underlying chemistry, if a metric can be developed for quantifying the
degradation.
Attempts have been made to analyze and model various aspects of this
problem. Mass loss rates have been empirically fit to Arrhenius rate curves
[3].
Arrhenius rate kinetics represent an important, established method of
reporting and comparing kinetic data.
The Arrhenius rate equation
expresses material conversion/degradation rate as a function of both
temperature and conversion state. The true versatility of this model lies in
the generality of the conversion-dependence function used in the rate
equation, allowing a large variety of experimental rate measurements to be
modeled in this manner [1]. This type of approach provides a simple means
to model the stability of different systems but is useful only for comparative
purposes if data is not collected and reduced in a rigorous manner. Other
degradation models such as Coats/Redfern,
Ingraham/Marier, and
Horowitz/Metzger have also been fit to mass loss rate data [25].
These
models are less general than the Arrhenius form, placing specific
assumptions on the mechanisms which are being modeled. As such they are
less versatile than the Arrhenius approach and are more commonly used as
methods for comparing the stability of similar polymer systems subjected to
22
isothermal exposures than for determining kinetic parameters for predictive
modeling.
More sophisticated models have combined modeling of the diffusion of
oxygen into the material with chemical reaction rate equations to predict the
mass loss and growth of degraded surface layers.
In many such cases
effective diffusion coefficient models are used [26] where an apparent
diffusivity is found by fitting to experimental mass loss curves for a
composite.
Models of this kind allow the anisotropic nature of the
degradation to be simulated but offer little insight to the true physics of the
problem, effectively smearing many possible mechanisms together into the
observed global effects.
Hinkley and Nelson [27] conducted tests on unidirectional LaRCTM-160
and PMR-15 graphite composite for up to 25,000 hours. They used Arrhenius
plots as empirical fits to obtain ranges of activation energy in a temperature
band of 160-180 0 C.
They were able to obtain reasonable lifetime
extrapolations but did not succeed in capturing the underlying degradation
mechanisms.
Nam and Seferis [28] developed a generalized methodology for
composite degradation based on two elementary reaction mechanisms, hence
allowing for both reaction and diffusion controlled degradation mechanisms.
Several independent reaction mechanisms may be accounted for through the
use of weighting factors. These weighting factors assign certain proportions
of the overall mass loss to individual reactions, each with its own set of
kinetic parameters, and thus allow a variety of complex chemical degradation
processes to be modeled.
2.4
RECENT WORK
Most of the tests of this material exposed to a high temperature
oxidative environment are difficult to interpret because of the coupled nature
of the various degradation mechanisms and the non-uniformity
degradation.
of
Tests are accelerated using temperatures and/or pressures
higher than test conditions. However, the scaling factors associated with
such tests are not well understood. It is not clear, for example, that diffusion
and/or different chemical reactions will scale with temperature in the same
way.
Models which can calculate [29] degraded composite laminate
properties and behaviors based on known degradation states within the
material have been developed.
However, these models require accurate
degradation and diffusion information, and require careful verification at all
levels before they will be useful for predictive calculations.
The understanding of diffusion has substantially improved in the light
of recent work. Cunningham [1] recorded the formation of degraded surface
layers as functions of exposure time using photomicrographs at different
temperatures.
Geometry effects in the neat resin, and anistropic diffusion
effects in the composites, were identified using specimens with different
aspect ratios. The diffusion coefficients were calculated using this data.
The chemical degradation, though well understood, has not been
accurately quantified due to the complex degradation chemistry of PMR-15.
Thermogravimetric analyses (TGAs) were conducted on powdered specimens
in nitrogen and air to separate the thermal reactions from the oxidative
reactions. Tests were also carried out in oxygen to understand the effects of
oxygen concentration on the degradation process. All these tests were carried
out on powdered specimens to decouple the diffusion effects from the
24
chemical effects.
This work suggested that thermal reactions are made up of a spread of
a large number of low mass fraction reactions, although the behavior at
higher temperatures can be approximated using two effective Arrhenius
reactions.
These reactions die out rapidly as the temperature is lowered
towards the use condition and so it may not be necessary to capture the
behavior of these reactions with great accuracy.
Oxidative reactions are extremely active at test temperatures, and are
also of concern at use temperatures.
These reactions are concentration
dependent and appear to consist of multiple reactions which have different
rate and concentration dependencies.
The confounded nature of these
reactions makes it difficult to quantify the mass fractions on which they act.
These reactions dominate the low temperature behavior and so an accurate
representation of their behavior is needed. Cunningham [1] used high rate
dynamic TGA tests to extract a preliminary set of modeled chemical
reactions, but accuracy was limited, and extrapolation to use conditions was
found to be unfeasible. The use of a test program that used large number of
isothermal TGAs along with very low rate (below 1°C. min.) dynamic heating
tests was recommended.
Isothermal TGAs on powdered specimens in nitrogen, air and oxygen
[30] yielded activation energies in air which were approximately one-half of
those in nitrogen, indicating that significantly less energy is required for
oxidation as opposed to thermal degradation. Comparison between tests in
air and oxygen have revealed a strong effect of relative oxygen concentration
on reaction rate, with rates being greatly accelerated with increasing oxygen
concentration. However, only comparative data was detailed in this study,
data was not reduced to a set of kinetic coefficients which could be used in
25
analytical models.
Another way of attacking this problem is the simultaneous use of two
or more techniques focused on studying the chemical phenomena. Liau et al
[31] studied a organic polymer resin called Poly(Vinyl Butyral). Weight loss
curves were fitted to an Arrhenius type equation and each reaction was
identified from its major evolving gas. The amount of gases evolved were
measured using Fourier Transform Infrared Spectrometry (FTIR). However,
data from FTIR will be difficult to interpret in the case of polymers like PMR15, in which multiple reactions lead to the formation of the same byproducts
such as CO2, CO and H20.
Jordan and Iroh
[32] used gravimetry, differential scanning
calorimetry (DSC) and FTIR to study the isothermal aging of partially
imidized LaRC-IA polyimide resin. Qualitative information can be obtained
from spectral assignment of intermediate and final reaction products, while
quantitative evaluation of the spectra recorded in a predetermined time
interval provides the basis for the determination of reaction kinetics. The
time dependent intensity changes, measured at different temperatures
provide the data used to determine the reaction kinetics.
The authors
collected the relevant data but did not demonstrate its use for obtaining the
reaction constants.
Another factor left untouched in most of the other work is the effect of
fabrication parameters on the degradation process.
Weisshaus and
Engleberg [33] studied ablative composites used as thermal active insulation
used in rocket nozzles. They measured failure mode and tensile strength at
temperatures
from ambient to 9000 C for samples which had been
manufactured by the same process, but with different levels of forming
pressure and heat treatment. This study suggested that fabrication method
26
can have an impact on the degradation level because it can influence the
chemistry by leading to different levels of imidization in the polymer.
It is clear that the need for a more accurate kinetic reaction model still
remains. The degradation behavior at use temperatures (150-250'C) needs to
be well understood.
The quantification of oxidative reactions is more
important than that of thermal reactions as material is exposed to air when
in use, and also because their effects outweigh those due to purely thermal
reactions.
CHAPTER 3
PROBLEM STATEMENT AND APPROACH
3.1
PROBLEM STATEMENT
The focus of this research is to develop a model of the chemical
degradation of a polymer matrix composite such that, given the external
chemical environment and temperatures throughout the laminate, laminate
geometry, and ply and/or constituent material properties, and the
concentration of diffusing substances throughout, we can calculate the
metrics of chemical degradation, as functions of time and position throughout
the laminate.
3.2
APPROACH
The approach consists of both analytical and experimental work. The
analysis provides insight into the physical mechanisms and can be used for
building models. These models are also useful for interpreting and reducing
test data. The ultimate goal of the analysis is to provide a capability for
predicting composite degradation behavior.
Experiments improve the
understanding of the chemical degradation in service conditions, and allow
the building of an advanced model that eliminates the shortcomings of the
previous models. Long term isothermal tests were conducted at various
temperatures.
The experimental data was utilized for obtaining the
coefficients of the advanced analytical model and provided verification of the
analytical approach. The data, along with the previous work, also provided
28
useful insights for future testing.
3.3
ANALYTICAL TASKS
The analysis comprises a basic chemical reaction model. An Arrhenius
reaction model is used for describing the thermal and oxidative reactions.
Mass loss (or gain) is used as a degradation metric.
The entire mass is
divided into smaller mass fractions, some of which do not react. Each of the
reacting mass fractions is assumed to be attacked by one chemical reaction
which alters the amount of mass remaining after thermal exposure. Three
different reactions are considered. Two lead to mass loss, and one leads to
mass gain. A negative mass fraction is used to model the mass gain behavior
observed during experiments. The analysis includes the temperature range
for which experiments were conducted (150 to 300'C).
The analysis is implemented through the use of an explicit time-step
Inputs to the analysis are the exposure
finite difference computer code.
temperature as a function of time. Degradation states within the material
are calculated as functions of exposure time. The analysis was used to reduce
mass change data from aging experiments on powdered specimens to a set of
chemical reaction constants.
Finally, model predictions incorporating
chemical reactions were correlated with the mass loss data obtained in aging
tests conducted during the course of this research, and also some of the
experimental results from tests on neat resin powder carried out by
Cunningham [1].
3.4
EXPERIMENTAL TASKS
All materials used in the course of this research were manufactured at
the NASA Lewis Research Center.
29
Neat PMR-15 resin samples are
considered. Isothermal tests on powdered resin specimens are carried out in
both inert and oxidative environments.
The use of powders allows the
decoupling of purely chemical effects from diffusion controlled effects. The
inert atmosphere is used so as to provide data for the purely thermal effects.
A new low cost test method is developed, and tests are carried out for a large
variety of conditions, for up to 200 hours. The results, and the correlation
with the analysis, provide insight into accurate methods for determining
aging behavior in this class of materials.
CHAPTER 4
ANALYTICAL METHODS
The basic analytical approach is described in this chapter.
The
chemical reaction model used for quantifying the degradation is explained
here.
The model uses Arrhenius type of reactions to describe the mass
changes in the material. The procedure for reducing test data to obtain the
reaction coefficients, and the method for implementing the model, are
detailed.
4.1
DEGRADATION MODEL
Chemical reactions are used to model the degradation behavior. The
analytical treatment given here is similar to that used by Cunningham [1]
and McManus and Chamis [29]. The reactions are considered to take place
inside an infinitesimal control volume containing a mass mo of matrix
material.
The fibers are assumed to be stable.
The matrix material is
assumed to consist of different components that are available for various
reactions. A mass mi is defined as the mass that would be lost (or gained)
due to the completion of a set of reactions involving component i. A mass
fraction y, is defined as the ratio between the mass of component i and the
overall mass
(4.1)
y = i
m
negative
A
fraction
mass
to
used
is
indicate
o the amount of mass added due to
A negative mass fraction is used to indicate the amount of mass added due to
a weight gain reaction.
A conversion metric a i is used to quantify the
degradation of mass fraction yi. When a, is equal to zero, no degradation has
taken place; when a i is equal to one, the mass fraction is entirely lost (or
gained). The rate at which mass changes from the control volume due to
degradation of component i is
o-
i
dt -
i
yi dt
(4.2)
Note that summation notation is not used here. The total mass change for
component i, over a time period t is given by
t 8dm
Ami = -dt
(4.3)
Finally, the mass change for the control volume is
Am =
Ami
(4.4)
all i
All of the above considers the mass loss at a point within the material,
which is not a measurable quantity. In a finite specimen of volume V, we
measure the total mass change and mass change rate
AM = AmdV
(4.5)
V
d(AM)
d(Am)dV
(4.6)
Finally, in some cases certain mass fractions will not react. A final
mass mf is defined as the sum of the unreacting mass fractions
mf = m o
.yi
(4.7)
tcunreacting
A normalized mass change, which reaches a value of one when all reactions
have completed, is then defined as
Am' =
m o - mf
(4.8)
The conversion metric, a,, is defined here in terms of the normalized mass
change for each component i at any time t
ai =Am/
(4.9)
Ai
mo, - mfi
where moi and mi represent the initial and final masses of component i
respectively.
For weight adding reactions moi= 0, and for weight losing
reactions mi = 0.
Arrhenius reaction kinetics are assumed for the chemical reactions
acting on the different mass fractions.
Reaction rates for each material
component i are related to the conversion metric, a,, and to the absolute
temperature, T, by different and independent functions. A complete kinetic
description of a chemical reaction requires the characterization of both, the
rate (temperature-dependence) function F'(T), and
dependence function F(ai) [6].
the conversion-
Generally, reaction rates increase with
temperature. At high values of ai the reaction rate will typically slow down
due to the decreasing amount of material available to the reaction.
The rate constant F'(T) is a function of temperature only, whereas
F(ai) is some function of conversion, a i. Typically, F'(T) is assumed to follow
an Arrhenius-type expression, and so
F'(T)= kiexp(-Ei
RT
(4.10)
where ki is the reaction rate constant defining the frequency of occurrence of
the particular reaction configuration, E is the activation energy which
represents
the energy barrier that must be surmounted
during
transformation of reactants into products, and R is the real gas constant.
F(a,) is commonly expressed as (1- a,)"' assuming nth-order kinetics, giving
33
= k,(1- ai)" i exp
dt
(4.11)
RT
In cases where the reactions are controlled by the concentration of a diffusing
substance, a modified form of Eq. 4.11 is used
da=k,(l- a)"' cs exp(-Ei
dt
(4.12)
RT
-
where cs is the concentration of the diffusing species and m, defines the order
of the concentration dependency.
All of the expressions derived thus far assume that only a single
reaction acts on each of the mass fractions.
For the general case where
multiple reactions can occur, each mass fraction yi can be attacked by a
number of reactions j.
The reactions rates in, say, an oxidative atmosphere
can then be fully described by
dt
- k i(1- a i )n cmii exp
S.f
(4.13)
RT)
where cS is the concentration of the diffusing oxygen. Again, summation is
not implied here. The reaction rate constant k, , activation energy E1j, and
reaction order nij are needed to fully characterize each reaction. The oxygen
concentration dependence mij is zero for thermal (non-oxidative) reactions,
and must be specified for oxidative reactions. The reduction of mass fraction
of component i is calculated from
dai
daiJ
(4.14)
idt
(4.15)
allj
ai
=
Note that none of the quantities in here are tensors. The notation
employed in these equations was chosen as a convenient method in which to
express the occurrence of multiple, simultaneous reactions.
34
This is the
general form of the chemical degradation model. The specific model used in
this research considered that only one chemical reaction acted on each
component. The additional complexity of multiple reactions acting on each
component was not required to model the observed chemical reactions.
4.2
DETERMINATION OF KINETIC CONSTANTS
No standard method is available in the literature for determining
kinetic constants from mass loss data for isothermal tests.
Reaction
constants for the model were obtained by reducing the data using curvefitting techniques.
The mass loss/gain data collected from isothermal tests in air suggests
that a minimum of three reactions are required to describe the chemical
degradation. Determining the mass fraction on which each reaction acts, and
the three kinetic constants that specify each reaction, is necessary for
completely describing the model. Each reaction is described using three
constants: activation energy E,, order of reaction ni, and rate constant Ki,
where
Ki = kicms,
(4.16)
and cms ' is constant because the oxygen concentration does not change as a
function of time or position.
Observed experimental data, detailed in Chapter 6, indicated the
presence of two reactions acting on relatively small mass fractions and a
reaction acting on a large mass fraction. Once of the small mass fraction
reactions led to mass gain. The mass gain reaction was modeled using a
Arrhenius type of reaction acting on a negative mass fraction. None of the
previous models include mass gain behavior.
35
The small mass fraction
reactions with mass loss (reaction 1) and mass gain (reaction 2) showed
saturation behavior (no more mass loss or gain is seen). The mass fractions
for these reactions were determined using the normalized mass loss/gain seen
at saturation stage.
The large mass fraction for the third reaction was
estimated using a numerical search. After the mass fractions were obtained
the kinetic constants were determined using a curve-fitting procedure in two
steps. The details of this curve fitting procedure are described in section 4.4.
4.3
MODEL IMPLEMENTATION
The model was implemented for an infinitesimal volume subjected to
isothermal heating in air. Three reactions were considered, all of which were
assumed to be oxidative. As the tests were conducted on powdered material
in air, no variation in the oxygen concentration was considered.
conditions consisted of ai= 0 for all three reactions.
Initial
The reaction rate
constant K i as described in Eq. 4.16 was used. E, ni, and K were specified for
each reaction along with time t. The rate of reaction was calculated using Eq.
4.12 and then multiplied by the corresponding mass fraction (Eq. 4.2) to get
the rate of change of mass for each reaction. The rate of mass change for
each reaction was then integrated over time t (Eq. 4.3) and then summed to
obtain the total mass change (Eq. 4.4). Reactions that showed saturation
reached state a,=1 and then the reaction state did not change. All the mass
changes were calculated as normalized mass loss or gain. The model was
implemented using an explicit time-step finite difference computer code
4.4
DATA REDUCTION IMPLEMENTATION
Observation from the experimental data showed the presence of a
minimum of three different reactions. There is a possibility of more than 3
36
reactions being active in this temperature range (150-300'C), however it was
thought that three reactions would be sufficient to model the degradation
behavior observed in these isothermal aging tests.
The coefficients for the three reactions in the model and the mass
fractions on which they act were obtained from the experimental
observations.
We assumed a small mass loss reaction (see 150 0 C), a small
mass gain reaction (see 175-200'C), and a mass loss reaction that affected a
large mass fraction. The saturation behavior seen in 150-200'C test was
utilized for obtaining the mass fractions for the two small mass change
reactions. The large mass fraction for the third reaction was estimated using
a numerical search. No distinction was made between thermal and oxidative
reactions. All reactions were modeled as being of the form
dai = Ki(1-ai)n ' exp(-i )
dt
RT
(4.17)
where K is defined in Eq. 4.16 for an oxidative reaction. In case of a thermal
reaction, K i = k i was assumed.
The three coefficients for each reaction
consisting of rate constant K, reaction order ni, and activation energy E were
estimated using an optimization procedure in two steps. In the intermediate
step, each reaction was modeled using C and n, where
Ci =Ki exp(- i
(4.18)
Each reaction was described as
ai = Ci(1- ai)n '
(4.19)
The degradation state for each reaction was determined using the explicit
time-step finite difference formulation
ai(t + At) = ai(t) + -
(t) x At
(4.20)
where a i = 0 at t = 0.
The reaction state calculated in this manner was
multiplied by the respective mass fraction for all the reactions to obtain the
total normalized mass loss/gain. These results were compared with the data
obtained from experiments and the least squares error was calculated.
Values for Ci and n were obtained by minimizing the least squares error for
each temperature.
This was carried out for data at all the seven test
temperatures (150-300'C in steps of 25°C). The n values were found to be in
a narrow range for each reactions, as expected. The reaction order in the
Arrhenius type of reaction does not change with temperature. The values
obtained for Ci varied a lot because of the strong dependence on temperature.
The MATLAB code utilized for this purpose is given in Appendix A along
with all the other codes used during the course of this research.
In the next step, each reaction was quantified using all the three
coefficients Ki, n, and E i .
The reaction states for each reaction were
calculated using the finite difference formulation from the previous step. The
normalized mass loss (or gain) was obtained as in the previous step.
Estimates of mass change were obtained for all the seven temperatures and
then compared to the experimental data. The least squares error obtained
from comparison with each data set was normalized by the mean mass
change for that temperature. The sum of such normalized least squares error
for all the data sets was used as the error function. This error function was
minimized using a standard optimization tool available in MATLAB (version
5.2).
Constraints were placed on the values of reaction order as per the
ranges obtained in the previous step. This constrained optimization is solved
using the Levenberg-Marquardt method by the optimization tool.
The
coefficients so obtained were used for further comparisons of the model with
data from previous researchers.
CHAPTER 5
EXPERIMENTAL PROCEDURES
Experiments were carried out to obtain data for the chemical
degradation model described in Chapter 4.
The data obtained from
experiments gave valuable insights into the physics of the problem in
addition to helping obtain the reaction and mass fraction coefficients.
The
new cost-effective experimental method is described along with details about
specimen preparation, the set-up and data collection.
Only neat PMR-15
resin samples were used.
Only neat resin specimens in powder form were used in this
investigation. The test matrices were designed based on recommendations by
Cunningham[1], and the fact that the in-use temperature range for this
material is from 150 to 2500 C. The material is also known to give off noxious
fumes at a temperature of 350'C and beyond.
Cunningham [1] had also
recommended the use of specimens with large surface area to volume ratios
in determining kinetic parameters.
Reaction coefficients estimated from
experiments conducted on finite-sized specimens may be confounded because
of diffusion effects.
Oxidative reactions were shown to be limited by the
amount of oxygen available and hence powdered specimens were utilized for
eliminating the diffusion effects. The test matrices were designed in such a
way as to allow the necessary coefficients to be extracted from the data and
also to provide sufficient data to allow a complete validation of the modeling
approach.
The material systems used in this study was PMR-15 neat resin. All
materials were manufactured at the NASA Lewis Research Center. The
material was initially cured in plates and was then reduced to powder form.
This ensured that the initial chemical state of the material was the same as
that used in real structures. The test matrix used for the isothermal heating
experiments is shown in Table 5.1. Isothermal heating experiments were
carried out on PMR-15 neat resin powder in nitrogen and air. This was done
with the aim of allowing the quantification of the kinetic parameters in both
thermal and oxidative atmospheres without the additional complexity
introduced by diffusion dominated effects.
5.1
MATERIAL MANUFACTURE AND PREPARATION
All specimens were manufactured at the NASA Lewis Research Center
using standard manufacturing procedures developed for the PMR polyimides.
The details of these procedures may be found in [34]. Two PMR-15 neat resin
panels (both 102 mm x 102 mm and approximately 3 mm thick) were used
during this study. After curing, all panels were subjected to a 16 hour freestanding post-cure in air at 316 0 C.
Narrow strips (approximately 5 mm wide) were cut from the neat resin
panels using a clean, sharp knife edge. These strips were then broken into
several small pieces and placed into a standard coffee grinder. To avoid the
problem of plastic shards from the grinder blade casing contaminating the
material ( as previously encountered by Cunningham [1]), a grinder with
metal casing was obtained. A custom steel lid was manufactured for use
instead
of
the
plastic
cover.
Specimens
were
subjected
Table 5.1
Neat ResinA Isothermal Exposure Test Matrix
Atmosphere
Isothermal Exposure temperature
Air
Nitrogen
125 0 C
1
1
150 0 C
1
175 0 C
1
200 0 C
1
225 0 C
1
250 0 C
1
275 0 C
1
300 0 C
1
A
All specimens in form of fine powders.
1
1
to grinding for about five minutes. The grinder was turned off after every
two minutes for about thirty seconds to avoid over-heating the motor. The
powder which was produced in this manner was then sifted through
calibrated sieves to obtain the required grade of powder for analysis. A fine,
light-brown powder was obtained from each sample through the use of this
technique.
Tests conducted by Cunningham [1] had indicated that the
particles obtained through the use of a No. 40 USA Standard Testing Sieve
(425 micron grating) were sufficiently small to ensure that the effects of
diffusion on the weight loss behavior in oxidative environments would be
negligible. All of the powder was sifted through a No. 40 sieve.
All powders produced in this manner were placed in small, unsealed
glass jars into the oven for 2 hours at 125°C to remove any residual moisture.
Due to the large surface area of the particles, the removal of moisture from
the powder is achieved in small amounts of time. This large surface area also
has a secondary effect which is to allow moisture to diffuse very quickly back
into the powder. The neat resin powder was found to be very hygroscopic,
rapidly absorbing moisture from the air upon removal from the oven. The
glass jars were immediately sealed after removal from the oven and the
powder was stored like this until testing.
5.2
EXPERIMENTAL PROCEDURE FOR ISOTHERMAL TESTS
5.2.1 Experimental Set-up
All powdered neat resin samples were aged in a thermal environment
chamber.
The chamber used electric resistance rods for heating and a
maximum temperature of 427°C could be achieved. A stainless steel rack
made using four rods and three rectangular plates with holes, was used to
support the specimens within the chamber. The powdered sample was placed
in an aluminum pan (dia. 35 mm) in the same location close to the chamber
bottom for each test. Internal chamber dimensions were 30.2 cm x 10.2 cm x
10.2 cm (12" x 4" x 4"), and the sample pan was placed at a height of 3" from
the bottom..
A schematic of the set-up is shown in Figure 5.1.
The
specimens were shielded from direct heat radiation from the heating rods and
were heated by fan-circulated air only. The temperature of the chamber was
controlled through the use of an Omega temperature controller.
This
microprocessor-based controller could be programmed to any user-defined
thermal profile consisting of a series of linear segments. A single J-type
thermocouple provided feedback to the controller. The temperature gradient
between the sample pan location and the controller thermocouple was
minimized. Over 100 tuning runs had been carried out in a previous study to
determine the optimum controller tuning settings and feedback thermocouple
location [35]. These settings were not altered in the current study.
5.2.2 Tests in Air
A clean aluminum pan, spatula and pincers were used for each
experiment. This apparatus was cleaned with water and than with methanol
and then dried for 15 minutes in a clean-air hood. A new pan was used for
each experiment. The steel rack and inside of the chamber were cleaned
using a wet paper towel before each experiment. The chamber was then
heated to 125°C and held there for 15 minutes before starting the
experimental run.
- Steel stand
Aluminum pan with sample
Control Thermocouple
Figure 5.1
Schematic of specimen and thermocouple location in thermal
environment chamber (not to scale).
AE 100 Mettler balance with a least count of 0.1 mg was used for weighing
the pan and sample. The clean pan was weighed first, and then a sample of
about 600 mg was placed in it. A spatula was used for removing the powder
from the glass jars. The weighing balance was recalibrated and its leveling
checked before each experiment. The sample pan was moved using pincers
only, and the pincers were cleaned periodically and kept free of dust
throughout the experiment. The pan was placed on the lowest shelf inside
the chamber. The sample was then heated to 125oC and held for two hours.
The pan was removed from the chamber and weighed at the end of these two
hours.
The sample mass obtained from this measurement was utilized
during all further calculations. The temperature was then ramped up to the
test temperature and then held there for a duration in excess of 200 hours.
The sample pan was removed periodically for weight measurements.
The chamber door was opened, the pan was removed, and the door was
immediately closed. The pan was then weighed using the sensitive balance
and then put back into the thermocycling chamber. This procedure lasted
less than a minute. The test chamber temperature dropped because the door
was opened twice during each measurement. However, the test temperature
was restored in less than five minutes due to the large thermal mass of the
chamber. As tests were conducted in excess of 200 hours, and readings taken
with an average gap of six hours (360 minutes) this temperature drop was
not considered in further calculations and the sample was assumed to be at a
steady temperature throughout the duration of the test.
A test was conducted in which a pan with powdered resin sample was
held at 125°C for over 200 hours. No reactions are known to occur at this
temperature and this experiment was conducted to study the extent of
possible scatter and any other sources of error. The weighing balance takes a
few seconds to give a steady reading. This reading can be affected by any
potential moisture absorption during this period. The readings showed a
variation of +1.0 mg to -1.1 mg. Lack of any trend in this data showed that
the sample was not being blown away by the circulation fan and that error
due to sources such as moisture absorption was small (0.2%).
5.2.3 Tests in Nitrogen
Additional parts were used in the set-up for conducting isothermal
tests in nitrogen.
Nitrogen cylinders with 5 PPM impurities were used
during these test. The cylinder was connected to a two-stage regulator. The
maximum pressure of gas in the cylinder was 2000 psi. The second stage had
a delivery pressure from 0 to 150 psi. The gas was then fed to a flowmeter,
which was then connected to a tube.
The gas passed through a
moisture/oxygen trap before reaching the solenoid valve on the thermocycling
chamber. The trap had a specification of 0.5 PPM impurities. A schematic of
the setup used for tests in nitrogen is shown in Figure 5.2. The gas pressure
was maintained 40-50 psi above the atmospheric pressure and the gas flow
was increased (from 596 ml/min. to 913 ml/min.) during the time of sample
removal for weight measurement. The gas was maintained at a pressure to
avoid any air leaking into the chamber during the experiment. The effect of
air exposure during the weight measurements was assumed to be
insignificant. This assumption was found to be incorrect after data from
three different runs was reduced. The details of this error are discussed in
Chapter 6 (Results).
46
Input pressure
up to 2000 psi
Delivery pressure
0 to 150 psi
Figure 5.2
Schematic of atmosphere control system for aging tests in inert
atmosphere
CHAPTER 6
RESULTS AND DISCUSSION
In this chapter the experimental data and the analytical results
obtained from the model are presented. Long term isothermal tests were
conducted in oxidative environment (air) and also in purely thermal
environment (nitrogen). The data from tests in air was reduced to obtain the
kinetic reaction coefficients, which served as input to the analytical model.
The model was correlated with this data.
A combined model, using this
model with parts of the previous model of Cunningham [1] was used for
correlating with some of the previous TGA data.
6.1
LONG TERM ISOTHERMAL AGING TESTS IN AIR
Isothermal aging tests in the oxidative environment were conducted
for temperatures of 125 to 300°C in steps of 25°C. This temperature range
was selected because the service conditions for this material range from 150250°C. The results obtained are presented in the form of normalized mass
loss plotted against time in hours. This data was then reduced using the
procedure described in Chapter 4. A comparison of model predictions using
these coefficients with the isothermal aging data is also presented.
6.1.1 Experimental Data
All tests were conducted on powdered specimens in order to separate
the diffusion effects from the reaction chemistry. Each sample was heated at
48
125"C for two hours before it was heated to the test temperature and held
there for a duration in excess of 200 hours. The sample mass measured at
the end of two hours of heating was used as the original mass.
The
normalized mass loss Am,(t) at time t was calculated using
Amn(t) =
- M(t)
Mo
(6.1)
where M o is the original sample mass, M(t) is the sample mass measured at
time t.
A long term isothermal aging test was carried out at 125°C to estimate
the experimental error. No reactions are known to occur at this temperature
and this test was conducted to study the extent of possible scatter and any
other sources of error. The sample was removed from the thermocycling oven
for mass measurement periodically.
atmosphere during this measurement.
The sample was exposed to the
The actual process of taking a
measurement took a few seconds, mostly to allow the weighing balance to
give a steady reading. The reading can be affected by any potential moisture
absorption during this period.
For a sample mass of about 600 mg the
readings showed a variation of +1.0 mg to -1.1 mg. The normalized mass loss
results obtained from this test are given in Figure 6.1. Lack of any trend in
this data showed that the sample was not being blown away by the
circulation fan and that error due to sources such as moisture absorption was
small (0.2%).
Experimental results obtained from tests at different temperatures are
shown in Figures 6.2 to 6.8. The test conducted at 150"C clearly shows the
presence of a small mass fraction reaction, see Figure 6.2. After a duration of
about 100 hours saturation behavior was seen (no further mass loss/gain).
The maximum normalized mass loss value was 7.2 x10 -3 . The mass fraction
49
0.002C
1250C
0
0.0015 S0
0.001C
0.0005
0.000C
0
0
-0.0005
-0.001 C
13
130
0
0
13
13O
131
-0.0015
13
-0.002C
Figure 6.1
0
50
100
150
Exposure Time (hours)
Isothermal aging test in air at 125°C
200
250
0.020
0
O
150 C
0.015F
0
_J
- 0.01C
)
a0
N
E
0.00
o
10
0
0
10
0
z 0.005
0.00(1
0
50
0
13
0 1
100
150
Exposure Time (hours)
Figure 6.2
Isothermal aging test in air at 150"C
200
0.005-
0.0001
c,
1
cn -0.005
N
i -0.010
E
z
-0.015
-0.020-
0
Figure 6.3
200
400
600
Exposure Time (hours)
Isothermal aging test in air at 175°C
800
0.005
0
200 OC
0.000
O
-0.005
-0.010
0lO
-0.015
-0.020
Figure 6.4
12PW
[0113
0
D
1
300
Exposure Time (hours)
100
200
Isothermal aging test in air at 200'C
400
0.030
0.025
[7
225 OC
0
13
0.020
0
-J
0
0
0.015
0
0
0.010
N
0.005
,
0
E 0.005
0
0
z
-0.005
-0.010
-0.015
Figure 6.5
W c
0
13g 13O
IMO0
300
200
100
Exposure Time (hours)
Isothermal aging test in air at 225°C
400
0.160
0.140
cn
(I
0
-Z
CD
0.120
SC3
0
z
250 C
0.100
---
0.080
0.060
E
3
0.040
0.020
t
Ii
o.oo00
-0.020'
Figure 6.6
I
0
200
I
800
600
400
Exposure Time (hours)
Isothermal aging test in air at 250"C
1000
0.160
0.1
0.1
cn
o0
0.1
cn
0.080
N
0.060
E 0.040
0
z
0.020
0.001
-0.020L
0
Figure 6.7
150
100
50
Exposure Time (hours)
Isothermal aging test in air at 275°C
200
0.160
P
3
0.140
300 OC
d:PO6
0.120
db3
0.100
0.080
0.060
F
0.040
/
0.0201
0.00oo
-0.020'0
Figure 6.8
150
100
50
Exposure Time (hours)
Isothermal aging test in air at 300 C
200
for this reaction was estimated using this saturation mass loss value. The
data from the aging test at 175C is given in Figure 6.3. These results show
the presence of a small mass fraction weight gain reaction. Mass gain is
shown as negative mass loss in this plot.
Saturation in the mass gain
behavior was observed after a duration of about 120 hours. The maximum
normalized mass gain seen has a value of 18 x10-3 . The mass fraction for the
weight gain reaction was estimated using this value. The results from the
aging test at 200oC, given in Figure 6.4, are very similar to that of the test at
175oC. However, the maximum mass gain value seen is lower at 14.9 x10 3,
suggesting the presence of an additional reaction that leads to mass loss. The
presence of an additional mass loss reaction is confirmed from the 225"C test
results given in Figure 6.5. A clear transition from the domination of the
mass gain reaction to the domination of mass loss reaction(s) is seen. Tests
at higher temperatures show increasing levels of mass loss. No saturation
behavior is seen in this case even after an aging period of over 1400 hours at
250 0 C, as seen in Figure 6.6. The tests at 275 0 C (Figure 6.7) and 300 0 C
(Figure 6.8) show higher levels of mass loss and a trend similar to that seen
at 250 0 C.
6.1.2 Data Reduction and Correlation
On the basis of experimental observations described in the previous
sub-section, it was decided to use a three reaction model. This model consists
of two small mass fraction reactions (reaction 1 - weight loss, reaction 2 mass gain) and a large mass fraction reaction (reaction 3 - weight loss).
The mass fractions for reaction 1 was estimated using the highest
normalized mass loss. value (7.2 x 10-3) seen in the test at 150oC. Based on a
trial and error fit, considering the fact that weight addition reaction was
slightly active, a mass fraction of 8 x10-3 was selected for reaction 1.
The highest normalized mass gain value seen was 18 x10 -3 . This mass
gain was achieved after the saturation of first mass loss reaction, hence a
mass fraction of 26 x10-3 was assumed for reaction 2.
The tests at higher temperatures did not show any peaks or
saturation. A numerical search for the mass fraction of reaction 3 in the
range of 0.20 to 0.45 was carried out and the value (0.30) that gave the least
root square error was used as the mass fraction for reaction 3.
Once the mass fractions were fixed, the kinetic constants were found
as per the procedure described in Section 4.4. The kinetic constants for the
three reactions are given in Table 6.1. These constants were presented in
[36]. The mass fraction for reaction 3 shown here is slightly different than
that presented in reference [36]. The current value gives somewhat better
correlation with the data. The effect is not large. Note that the original form
of reference [36] also contains an unfortunate error - the activation energies
are incorrect by a factor of 10! The constants presented here, and also in
reference [37], are correct.
The model was then implemented using these coefficients and
compared with the experimental data, as shown in Figures 6.9 to 6.15. The
model captures the mass loss (or gain) behavior quite well.
Mass loss
reaction domination at 150°C, followed by the mass gain reaction domination
at temperatures 175°C and 200oC, and then the transition to mass loss
reaction domination again, is captured.
The model however, does not
correlate well with the data obtained in the test at 300'C. It is thought that
Table 6.1
Coefficients for the new three reaction model
Mass fraction
Rate constant
Activation energy
Reaction order
Yi
KI
E i in KJ/mol
ni
1
0.008
12.8 x 108
109
1.0
2
-0.026A
8.67 x 10 s
124
2.1
3
0.300
9.65 x 108
155
3.6
A
negative mass fraction represents a mass gain reaction
0.01
CO
O
0.0
-0.00
-
00
Figure 60.00
100
200
300
400
Exposure Time (hours)
Model comparison with isothermal aging test data in air at
150"C
0.010
0
0.005 o0
00
oo
.-0.005
0
cr
-0.005
0
0
0
100
200
300
400
Exposure Time (hours)
Figure 6.10
Model comparison with isothermal aging test data in air at
175 0 C
0.005
o
I
70
-0.005
-0.015 -
0
Figure 6.11
300
200
100
Exposure Time (hours)
400
Model comparison with isothermal aging test data in air at
200 0 C
0.025
0.020
cn 0.015
o
-J
cn
0.010
0.005
N
-F
0.00
0
z -0.005
0
-0.010
-0.015
Figure 6.12
-
0
300
200
100
Exposure Time (hours)
400
Model comparison with isothermal aging test data in air at
225 0 C
0.1400.120
0.100
0.080
0.060
0.040
0.020
0.00
-0.020
Figure 6.13
-
0
300
200
100
Exposure Time (hours)
400
Model comparison with isothermal aging test data in air at
250 0 C
0.20
0.15
0
-J
0.10
N
0.05
E
0.0
-0.05
0
Figure 6.14
100
200
300
400
Exposure Time (hours)
Model comparison with isothermal aging test data in air at
2750C
0.25
,
N
E
-jO
-0.05L
Figure
6.15
100
200
300
400
Exposure Time (hours)
Figure 6.15
Model comparison with isothermal aging test data in air at
300"C
this is because of a transition from low temperature behavior to differing
high temperature behavior.
6.2
LONG TERM ISOTHERMAL AGING TESTS IN NITROGEN
Long term aging tests in inert atmosphere were conducted at
temperatures 125°C, 200C and 300'C. Each of these tests was conducted for
a much shorter duration of about 20 hours, compared to aging tests in air,
because TGA tests conducted by Cunningham [1] in nitrogen had shown
saturation (or near saturation) behavior in 10 hours for tests at temperatures
300 0 C, 340°C and 380 0 C.
The experimental setup was modified for
controlling the atmosphere in the thermocycling chamber. The details are
discussed in Chapter 5. During the tests in nitrogen the sample was removed
from the chamber for weight measurement. The sample was exposed to air
for a period of about 30 seconds during each measurement. It was assumed
that this short exposure to oxidative atmosphere would not affect the sample.
However, this assumption was found to be incorrect.
At first, a test was conducted in nitrogen at 125 0 C to estimate the
scatter and the extent of any potential moisture absorption. The measured
mass loss varied from 0.0 to 1.2 mg. The lack of any trend in this data
showed that the sample was not being blown away by the circulation fan or
the nitrogen flow and that error due to sources such as moisture absorption
was small (0.3%). The results from this test are given in the form of a
normalized mass loss plot in Figure 6.16.
The results from the aging test in nitrogen conducted at 200C and
300'C are shown in Figure 6.17 and Figure 6.18. A high initial mass loss was
recorded in the test at 200 0 C, after which a clear mass gain trend was seen.
I
I
0.0030
o
125 OC
0.0025
0
-j
0.0020
0.0015
0
N
E
0
0.0010
z
0.0005
0.000ooo
10
20
30
Exposure Time (hours)
Figure 6.16
Isothermal aging test in nitrogen at 125°C
40
0.005
I
o
0
200 0C
0.004
o
0.003
I
-j(D
0.002
N
E 0.001
00
O
0
O
0.000
-0.001
Figure 6.17
II
0
10
II
40
30
20
Exposure Time (hours)
Isothermal aging test in nitrogen at 200"C
50
0.040
0.035
n 0.030
O
-I
n 0.025
S0 .0 2 0
N
F 0.015
E
0
z 0.010
0.0050.000.3
0
Figure 6.18
5
1
10
Exposure Time (hours)
Isothermal aging test in nitrogen at 300C
20
Mass gain cannot take place in an inert atmosphere. This showed that the
impact of exposure to oxidative environment was significant even when such
exposure was of a short duration. The test at 300°C (Figure 6.18) showed a
mass loss of 1.7% after aging for 3.5 hours. The mass loss seen after 10 hours
in nitrogen during isothermal TGA tests at 300'C was about 0.8% [1]. This
test also showed the impact of exposure to oxidative environment.
The
results from these tests were therefore assumed to be invalid, and were not
used for obtaining reaction coefficients.
6.3
COMBINED MODEL
A combined model was built using all the three reactions from the new
model and two thermal reactions from the previous model of Cunningham [1].
The previous model had three reactions (2 thermal and 1 oxidative). The
coefficients for this five reaction model are shown in Table 6.2.
reaction model captures the behavior at low temperatures.
The new
The thermal
reactions are active at higher temperatures.
The predictions using such a model were then compared with the data
from dynamic TGA tests in air conducted by Cunningham [1].
The
comparisons are shown in Figures 6.19 and 6.20 for two heating rates. The
combined model only roughly captures the TGA data.
In particular, it
predicts mass addition not seen in the data.
This shows that two different models cannot be combined in such a
manner to obtain a model that predicts the degradation behavior over the
entire range of temperatures. The TGA data shows that at the heating rates
used, no significant mass loss occurs at temperatures below 325oC. The new
model worked well for temperatures only up to 275 0 C, and therefore cannot
Table 6.2
Coefficients for the combined five reaction model
Mass fraction
Rate constant
Activation energy
Reaction order
Yi
Ki
E i in KJ/mol
ni
1
0.008
12.8 x 108
109
1.0
2
-0.026A
8.67 x 108
124
2.1
3
0.300
9.65 x 10s
155
3.6
4a
0.160
3.12 x 10 10
182
1.6
5b
0.240
7.9 x 1012
239
3.2
A
negative mass fraction represents a mass gain reaction
a, b
thermal reactions from the previous model
0.8
0.6
0o
(I
C')
0.
N
Cz
zE
o
0O
-0.11
100
Figure 6.19
200
400
300
Temperature CC)
500
Comparison of combined model prediction with 5oC/min.
heating rate TGA data in air
I
0.8
Combined Model
20 0 C/min data
0.7
u,
oO
I
U)
_0
I
0.6F
0.5
a)
U)
0.4
N
0.3
E 0.2
0
z
0.1
-
0.01
-0.10
0
100
Figure 6.20
200
400
300
Temperature CC)
500
Comparison of combined model prediction with 5oC/min.
heating rate TGA data in air
predict the behavior of oxidative reactions at higher temperatures. The TGA
data also explains why the previous model did not capture the behavior in
isothermal tests at lower temperatures. The coefficients for the model were
obtained by using TGA data which did not show any degradation behavior at
temperatures below 325 0 C.
The service conditions for PMR-15 like materials are in the range of
100 to 250 0 C. The present results suggest that the use of dynamic heating
TGA tests is not the best method for the study of degradation behavior in this
temperature region. The use of long term isothermal tests in air can capture
the degradation behavior in the lower temperature region. Such long term
aging tests can be conducted in a cost-effective manner as described in this
thesis. Long term isothermal aging tests in air can be used successfully to
characterize the material behavior for service conditions.
CHAPTER 7
CONCLUSIONS
New cost-effective experimental method
The newly developed experimental method is successful in measuring
the mass loss/gain behavior and is cost-effective for long duration isothermal
tests in air. The apparatus made use of a readily available thermocycling
oven and a temperature controller.
This method can be used for other
materials.
The method, when modified for tests in an inert atmosphere, had
limitations. The apparatus built from readily available components could
control the atmosphere, but the intermittent exposure to air during
measurements was a significant source of error. If the sample can be held in
an enclosed container during measurements, this apparatus might be useful
for tests in inert atmosphere.
Usefulness of long term isothermal aging tests
The data obtained from long term isothermal tests on powdered resin
material is useful in material characterization. The use of powder eliminates
the effects of diffusion. The mass gain behavior not seen in the previous
research on this material was captured using these tests. The detection of
apparent saturation behavior at some temperatures was especially useful,
because it led to accurate estimation of mass fractions for the chemical
reactions. Once the mass fractions were known the kinetic constants for the
Arrhenius reaction based model could be obtained with a high level of
confidence.
Success of new three reaction model
The new model adequately captured the behavior in the lower
temperature region (150-275 0 C). The in-use temperatures for PMR-15 are in
the range of 150-250 0 C. The collected data and this model can thus be useful
in the design of components using this material.
Limits of the new model
The new model could not capture the degradation behavior seen in
isothermal aging at 3000 C. The correlation of combined model with dynamic
heating TGA test data from previous work [1] is also mediocre. The behavior
at temperatures of 3000 C and higher is not captured; it is suspected that this
is due to fundamentally different reaction behavior at these higher
temperatures.
Recommendations
The experimental method used here should be able to characterize the
long term degradation behavior of high temperature resin materials. First
and foremost, the isothermal aging tests are able to capture the low
temperature chemistry. Also, the use of powdered specimens separates the
diffusion behavior from the chemical reactions, where the use of macroscopic
specimens would confound these two phenomena. This experimental method
is cost-effective, reliable and accurate and is recommended for the study of
other resin materials for high temperature applications.
REFERENCES
1.
Cunningham,
R. A.,
"High Temperature
Degradation
Mechanisms in Polymer Matric Composites", Massachusetts Institute of
Technology, S.M. Thesis, 1996.
2.
Bowles, K. J., Roberts, G. D., and Kamvouris, J. E., "Long-Term
Isothermal Aging Effects on Carbon Fabric-Reinforced PMR-15 Composites:
Compression Strength", NASA Technical Memorandum 107129, 1995.
3.
Kiefer, R., Yue, J. J., and Hinkley, J. A., "Kinetic Mapping of
Oxidative Weight Loss in Polyimide Composites", Journal of Advanced
Materials,Vol. 26, No. 3, 1995, pp. 55-59.
4.
Bowles, K. J., "A Thermally Modified Polymer Matrix Composite
Material With Structural Integrity to 371oC", NASA Technical Memorandum
100922, 1988.
5.
Reardon, J. P., "Beyond PMR-15", MaterialsEngineering,1992,
6.
Meador, M. A., Cavano, P. J., and Malarik, D. C., "High
Temperature Polymer Matrix Composites for Extreme Environments", Sixth
Annual ASMIESD Advanced Composites Conference, Detroit, MI, 1990, pp.
529-539.
7.
Foch, B. J., "Integrated Degradation Models for Polymer Matrix
Composites", Massachusetts Institute of Technology, S. M. Thesis, 1997.
8.
Alston,
W.
B.,
Gluyas,
R.
E.,
and
Snyder,
W.
J.,
"Cyclopentadiene Evolution During Pyrolysis-Gas Chromatography of PMR
Polyimides", NASA Technical Memorandum 105629, 1991.
9.
Bowles, K. J., Jayne, D., and Leonhardt, T. A., "Isothermal
Aging Effects on PMR-15 Resin", SAMPE Quarterly, Vol. 24, No. 2, 1993, pp.
3-9.
10.
Bowles, K. J. and Nowak, G., "Thermo-Oxidative Stability
Studies of Celion 6000/PMR-15 Unidirectional Composites, PMR-15, and
Celion 6000 Fiber", Journalof Composite Materials,Vol. 22, No. 10, 1988, pp.
966-985.
11.
Bowles, K. J., "Thermo-Oxidative Stability Studies of PMR-15
Polymer Matrix Composites Reinforced with Various Continuous Fibers",
SAMPE Quarterly,Vol. 21, No. 4, 1990, pp. 6-13.
12.
Bowles, K. J., "Effect of Fiber Reinforcements on Thermo-
Oxidative Stability and Mechanical Properties of Polymer Matrix
Composites", SAMPE Quarterly,Vol. 23, No. 3, 1992, pp. 2-12.
13.
Wong, M. S., Skontorp, A., and Wang, S. S., "Thermal Oxidation
of Carbon Fibers and Carbon-Fiber Reinforced High-Temperature Polyimide
Composite at Elevated Temperatures", ASC 9th Technical Conference,
Newark, DE, 1994, pp. 458-467.
14.
Alston, W. B., "Resin/Fiber Thermo-Oxidative Interactions in
PMR Polyimide/Graphite Composites", NASA Technical Memorandum 79093,
Cleveland, OH, 1979.
15.
Bowles, K. J., Jayne, D., Leonhardt, T. A., and Bors, D.,
"Thermal Stability Relationships Between PMR-15
Resin and Its
Composites", Journalof Advanced Materials,Vol. 26, No. 1, 1994, pp. 23-32.
16.
Scola, D. A. a. V., J.H., "Mechanical Properties and Mechanism
of the Degradation Process of 316 0 C Isothermally Aged Graphite Fiber/PMR15 Composites", Polymer Engineeringand Science, Vol. 31, No. 1, 1991, pp. 613.
17.
Roberts, G. D. and Lauver, R. W., "Quantitative Analysis of
PMR-15 Polyimide Resin by HPLC", Journalof Applied Polymer Science, Vol.
33, No. 8, 1987, pp. 2893-2913.
18.
Scola, D. A. and Vontell, J. H., "High Temperature Polyimides,
Chemistry and Properties", Polymer Composites, Vol. 9, No. 6, 1988, pp. 443452.
19.
Alston, W. B., "Characterization of PMR-15 Polyimide Resin
Composition in Thermo-Oxidatively Exposed Graphite Fiber Composites",
NASA Technical Memorandum 81565, 1980.
20.
Pater, R. H., Whitley, K., Morgan, C., and Chang, A.,
"Crosslinking-Property Relationships in PMR Polyimide Composites, Part I",
Polymer Composites, Vol. 12, No. 2, 1991, pp. 126-132.
21.
Alston, W. B., "Replacement of MDA with More Oxidatively
Stable Diamines in PMR-Polyimides", High Temperature Polymer Matrix
Composites, Cleveland OH, 1985, pp. 187-205.
22.
Roberts, G. D. and Vannucci, R. D., "Effect of Solution
Concentration and Aging Conditions on PMR-15 Resin", SAMPE Journal,
Vol. 22, 1986, pp. 24-28.
23.
Alston, W. B., "Structure-to-Property Relationships in Addition
Cured Polymers. IV - Correlations Between Thermo-Oxidative Weight Losses
of Norbornenyl Cured Polyimide Resins and Their Composites", NASA
Technical Memorandum 105553, 1992.
24.
Cella, J. A., "Degradation and Stability of Polyimides", Polymer
Degradationand Stability, 1992, pp. 99-110.
25.
Ansari, A. S., Turk, M. J., Alston, W. B., Frimer, A. A., and
Scheiman, D. A., "TGA/FTIR Determination of Polyimide Thermal-Oxidative
Degradation Kinetics", NASA preprint, 1996.
26.
Hipp, R. C., Harmon, D. M., and McClellan, P. S., "Accelerated
Aging and Methodology Development for Polymeric Composite Material
Systems", McDonnell Douglas Co. preprint, 1994.
27.
Hinkley, J. A. a. N., J.B., "Lifetime Extrapolation of PMR-15 and
LaRCTM-160 Graphite composites", Jpurnalof Advanced Materials,No. April,
1994,
28.
Nam, J.
D. and Seferis, J.
C., "Generalized Composite
Degradation Kinetics for Polymeric Systems Under Isothermal and
Nonisothermal Conditions", Journal of Polymer Science: Part B: Polymer
Physics, Vol. 30, No. 5, 1992, pp. 455-463.
29.
McManus, H. L. and Chamis, C. C., "Stress and Damage in
Polymer Matrix Composite Materials Due to Material Degradation at High
Temperatures", NASA Technical Memorandum 4682, 1996.
30.
Tsotsis,
T. K., "Thermo-Oxidative Aging of Composite
Materials", Journalof Composite Materials,Vol. 29, No. 3, 1995, pp. 410-422.
31.
Liau, L. C. K., Yang, T.C.K. and Viwanath, D.S., "Mechanism of
Degradation of Poly(Vinyl Butyral) using Thermogravimetry/Fourier
Transform Infrared Spectrometry", Polymer Engineeringand Science, Vol. 36,
No. 21, 1996, pp. 2589-2600.
32.
Jordan, K. M. a. I., J.O., "Effect of Isothermal Aging on Post-
Imidization and Glass Transition Temperature of LaRC-IA Polyimide Resin",
Polymer Composites, Vol. 18, No. June, 1997, pp. 397--404.
33.
Weisshaus, H. a. E., I., "High Temperature Properties of
Ablative Composites-l", Journalof Advanced Materials, No. January, 1996,
pp. 16-27.
34.
Boyd, J. D. and Chang, G. E. C., "Bismaleimide Composites for
Advanced High-Temperature Applications", 38th International SAMPE
Symposium, Covina, CA, 1993, pp. 357-365.
35.
Maddocks, J. R., "Microcracking in Composite Laminates Under
Thermal and Mechanical Loading", Massachusetts Institute of Technology,
S.M. Thesis, 1995.
36.
Patekar, K. A. and McManus, H. L., "Long Term Degradation of
Polyimide Composites", 8th U.S.-Japan Conference on Composite Materials,
Baltimore, MD, USA, to be presented,
37.
Patekar, K. A. and McManus, H. L., "Long Term Degradation of
Polyimide Composites", 98-9, Massachusetts Institute of Technology,
Cambridge, MA, USA, June, 1998.
APPENDIX A
MATLAB CODES
Files for fitting a 3 reaction model, with each reaction modeled using
two constants. The inputs to be specified are xo, the initial values for these
constants, and the number of iterations, options(14).
The other constants
specified are mass fractions, output file, input file containing the data (for
150 0 C data it is d150) inside the funct.m file that calculates the error between
the model and the data. Outputs are the best fit constants and the error
calculated.
%
File t2.m
% A constrained optimization approach to curve-fitting
% Intermediate step curve-fitting using only two constants per reaction
% The C constant is multiplied by le-7 inside the funct.m evaluation
tic;
x0=[1 2 3.2; 800 3 .0005];
% display paramters
options(1)=1;
% Max number of function evaluations
options(14)=100;
% Lower and upper limits on variables [ reaction order ; C ]
vlb=[ 0.8 1.9 3.16; 0.1 0.1 0.001];
vub=[ 1.2 2.3 3.24; 50000 5000 1];
% Matlab function for doing the optimization
[best]=constr('funct',xO,options,vlb,vub);
[error,g,yi,number,data,o_file]=funct(best);
[model] =sim_reaction(best(2,:),yi,best(1,:),data,number);
% generate a curve for the reaction_order numbers
plotdata(data,'ro',1);
hold on;
plotdata(model,'k-',0);
%printing output to a file specified inside funct.m
fprintf(o_file,'%9.3E ',best(2,:));
fprintf(o_file,'%6.5f ',yi);
fprintf(o_file,'%4.2f ',best(1,:));
fprintf(o_file,'%9.3E ',error);
fprintf(o_file,' \ n');
fclose('all');
toc; % for measuring the time taken by the code to run
% end of t2.m
% sim_reaction.m
function[model] =sim_reaction(C, yi, ni, data, number)
% This is a function for simulating multiple reactions and
% gives the total alpha
% Initialization and data set size determiniation etc.
deltat=1800;
r=size(data,1);
N=data(r,1);
Nu=N*(3600/deltat);
alpha(Nu,number)=0;
dalphadt(Nu,number)=0;
% Simulating the reactions using a finite difference scheme
for j= 1:number,
for i=l:Nu,
if alpha(ij) <= 1 & alpha(ij) >=O
% $$$$$$$ Factor of le-7 included in next line
dalphadt(ij)=C(j)*1e-7*(1-alpha(ij))^ni(j);
alpha(i+1j)=alpha(ij)+dalphadt(ij)*deltat;
if alpha(i+lj) > 1 alpha(i+lj)=l; end
if alpha(i+lj) < 0 alpha(i+lj)=0; end
elseif alpha(ij) < 0
dalphadt(ij)=0;
alpha(i+lj)=0;
elseif alpha(ij) > 1
dalphadt(ij)=0;
alpha(i+lj)=l;
end
t(i)=i*(deltat/3600);
end
end
alpha_T(1:Nu,1)=O;
% Sum the reactions metrics weighted by their mass fractions
for j=1:number;
alphaT=alpha_T+yi(j)*alpha(l:Nuj);
end
model(Nu,2)=0;
model(1:Nu,1)= [t'];
model(1:Nu,2)= [alpha_T];
% end of sim_reaction.m
% funct.m
% Defining a function that generates an error estimate
function [error,g,varargout] = funct(x)
% getting the data file of interest and setting the output file
load d200;
data=d200;
o_file='200.opt';
% Mass fractions
yi=[0.008 -0.026 0.35];
% Numer of reactions used in the model
number=3;
[model_pred] =sim_reaction(x(2,:),yi,x(1,:),data,number);
error=model_error(model_pred,data);
% It is necessary to specify these constraints
%g(1)=error-le(11);
%g(2)=-x(1,2);
%vararg(3)=-x(1,3);
%g(4)=-x(2,1);
%g(5)=-x(2,2);
%g(6)=-x(2,3);
% error has to be less than le-4
g(1)=error-le-4;
varargout{1)=yi;
varargout{2}=number;
varargout{3}=data;
varargout{4}=o_file;
% end of funct.m
% model_error.m
% Calculates the least sq. error between the model predictions
% and the data
function [terr] =model_error(model,data)
r=size(data,1);
deltat=1800;
err=0;
terr=0;
dum=0;
for i=1:10,
dum=data(i,1)*(3600/deltat);
err=sqrt((data(i,2)-model(dum,2))A2);
terr=terr+err;
end
for i=11:r,
dum=data(i, 1)*(3600/deltat);
err=sqrt((data(i,2)-model(dum,2))A 2);
terr=terr+ err;
end
terr=terr/r;
% end of model_error.m
%
****************************************************************
% plotdata.m
function[plt] = plotdata(data,x,type)
r=size(data,1); % Get number of rows for the data matrix
% type 1 for data and type 0 for model
if type == 1
plot(data(l:r,1),data(1:r,2),x,'MarkerSize',10,'LineWidth',2.0);
elseif type== 0
plot(data(l:r,1),data(l:r,2),x,'MarkerSize',3,'LineWidth',0.5);
end
% needed only for writing the axis labels
gca;
set(gca,'FontSize',18,'FontName','Helvetica','XLim', [0 700]);
xlabel('Exposure Time (hours)');
ylabel('Normalized Mass Loss ');
% setting the figure position on paper
%gcf;
%set(gcf,'PaperPosition', [1.25 2 4 4.5]);
%to make axis print in figure -- either make figure bigger, or...
axpos = get(gca,'position');
set(gca,'position',axpos+[0 .03 0 -.031);
% end of plotdata.m
****************************************************************
Files for doing the full scale optimization using all the 3 constants to
specify each reaction. Here, the inputs are all the constants for the three
reactions, the ranges in which they should be optimized, and the number of
iterations to be carried out. All these are specified inside the file bigt.m
which starts the optimization.
% bigt.m
% A constrained optimization approach to finding reaction coefficients
% Variables: reaction order, rate constant K, activation energy Ea
% Use of scaling factors to facilitate solution search
% for K it is le10
% for Ea it is 1e4
tic;
for i=1:3, figure(i); clf; end
% x0 is specified as, reaction orders, rate constants and then activation energy
% for all the 3 reactions
x0=[1.0 2 3.3; 0.10 0.10 0.10; 11 12.4 15.6];
% display paramters
options(1)=1;
% termination tolerance for f
options(3)=le-4;
m=100;
options(14)=m; % Max number of function evaluations
% Lower and upper limits on variables [ reaction order ; K, Ea ]
vlb=[ 0.9 1.0 2.5; 0.07 0.07 0.07; 10 11 14.8 ];
vub=[ 1.1 2.1 4; 0.25 0.25 0.25; 12 14 17];
[best] =constr('bigfun',xO,options,vlb,vub);
[terror,g,yi,number]=bigfun(best);
% Generating curves and model fits for all data sets
s=['d150' ; 'd175'; 'd200'; 'd225' ; 'd250' ; 'd275' ; 'd300'];
for i=1:7,
T=125+273+i*25;
a=s(i,:);
load(a);
data=eval(a);
[model]=simr(best(2,:),T,best(3,:),yi,best(1,:),data,number);
if i==l
figure(l);
plotdata(data,'ks',1);
hold on;
plotdata(model,'ro',0);
elseif i==2
figure(l);
plotdata(data,'kd',1);
hold on;
plotdata(model,'ro',0);
elseif i==3
figure(2);
plotdata(data,'ks',1);
hold on;
plotdata(model,'ro',0);
elseif i==4
figure(2);
plotdata(data,'kv',1);
hold on;
plotdata(model,'ro',0);
elseif i==5
figure(3);
plotdata(data,'kd',l);
hold on;
plotdata(model,'ro',0);
elseif i==6
figure(3);
plotdata(data,'ks',1);
hold on;
plotdata(model,'ro',0);
elseif i==7
figure(3);
plotdata(data,'kv',1);
hold on;
plotdata(model,'ro',0);
end
end
o_file='total.pt';
fprintf(o_file,'%9.3E ',best(2,:));
fprintf(o_file,'%5.3f ',yi);
fprintf(ofile,'%4.2f ',best(1,:));
fprintf(o_file,'%9.3f ',best(3,:));
fprintf(ofile,'%9.3E ',terror);
fprintf(ofile,'%3i',m);
fprintf(ofile,' \n');
fclose('all');
toc; % for measureing the time taken by the code to run
% end of bigt.m
%
*********************************************************
% bigfun.m
% A function to generate an error function over all the data sets
function [terror, g, varargout] = bigfun(x)
% Mass fractions
yi=[0.008 -0.026 0.20];
% Numer of reactions used in the model
number=3;
error=0;
terror=0;
T=0;
s=['dl50' ; 'd175'; 'd200' ; 'd225' ; 'd250' ; 'd275'; 'd300'];
% A mean of the data points is used as a scaling factor
scale_factor=[0.0046 0.0118 0.0092 0.015 0.0678 0.0659 0.0712];
% Just to give more weightage to d300 data
scale_factor(7)=scale_factor(7)/1.5;
for i=1:7,
a=s(i,:);
load(a);
data=eval(a);
T=273+125+i*25;
[model_pred]=simr(x(2,:),T,x(3,:),yi,x(1,:),data,number);
error=model_error(model_pred,data);
terror=(error/scale_factor(i))+terror;
end
% Total error has to be less than le-4
g(1)=terror-le-6;
varargout{}l)=yi;
varargout{2}=number;
% end of bigfun.m
% simr.m
% A function to implement the model
function[model] =simr(K,T,Ea, yi, ni, data, number)
% This is a function for simulating multiple reactions and
% gives the total alpha which make use of a full model using activation
% energy and temperature
% Initialization and data set size determiniation etc.
deltat=1800;
r=size(data,1);
N=data(r,1);
Nu=N*(3600/deltat);
alpha(l:Nu,1:number)=O;
dalphadt(1:Nu,1:number)=O;
R=8.314;
duml=0;
dum2=0;
dum3=0;
% Calculating the reaction coeff
for m=l:number,
duml=-Ea(m)*1e4;
dum2=R*T;
dum3=exp(duml/dum2);
C(m)=K(m)*lelO*dum3;
end
% Simulating the reactions using a finite difference scheme
for j=1:number,
for i=l:Nu,
if alpha(ij) <= 1 & alpha(ij) >=O
dalphadt(ij)=C(j)*(1-alpha(ij))A ni(j);
alpha(i+lj)=alpha(ij)+dalphadt(ij)*deltat;
if alpha(i+lj) > 1 alpha(i+lj)=l; end
if alpha(i+lj) < 0 alpha(i+lj)=0; end
elseif alpha(ij) < 0
dalphadt(ij)=0;
alpha(i+lj)=0;
elseif alpha(ij) > 1
dalphadt(ij)=0;
alpha(i+lj)=l;
end
t(i)=i*(deltat/3600);
end
end
alphaT(1:Nu,1)=O;
% Sum the reactions metrics weighted by their mass fractions
for j=1:number;
alpha_T=alpha_T+yi(j)*alpha(l:Nuj);
end
model(Nu,2)=0;
model(1:Nu,1)=[t'];
model(l:Nu,2)= [alphaT];
% end of simr.m
o ****************************************************************************
% model_error.m
% Calculates the least sq. error between the model predictions
% and the data
function [terr] =model_error(model,data)
r=size(data,1);
deltat=1800;
err=0;
terr=0;
dum=0;
for i=1:10,
dum=data(i,1)*(3600/deltat);
err=sqrt((data(i,2)-model(dum,2))A2);
terr=terr+err;
end
for i=11:r,
dum=data(i,1)*(3600/deltat);
err=sqrt((data(i,2)-model(dum,2))A2);
terr=terr+ err;
end
terr=terr/r; % dividing th error by the number of points of data
% end of model_error.m
% A functions to generate curves by loading the data and plotting it appropriately
% A function to plot different sets of data
% fig.m
a=char('d125','d150','d175','d200','d225','d250','d275','d300');
s=char('125
AoC','150 AoC','175 A^oC','200 A^oC','225 AoC','250 A^oC','275 A^oC','300 AOC');
% Specify a number between 1 and 8 to obtaint the appropriate figure
m=1;
figure(l);
for i=m,
load(a(i,:));
data=eval(a(i,:));
r=size(data,1);
plot(data(1:r,1),data(1:r,2),'ks','MarkerSize',10,'LineWidth',2.0);
hold on
end
axl=gca;
set(gca,'FontSize',18,'FontName','Helvetica');
%set(gca,'FontSize',18,'FontName','Helvetica','XLim', [0 200],'YLim', [-0.0020 0.002]);
xlabel('Exposure Time (hours)');
ylabel('Normalized Mass Loss ');
% To put a line at [0 0]
xlim = get(axl,'xlim');
1 = line(xlim, [0 0],'color','k','parent',ax1);
% To get formatted ticklabels
yt= 0:0.005:.04 ; % ticks
yl = sprintf('%.3f ',yt); %tick label with extra [
yl(end) = []; %without extra I
set(gca,'ylim', [min(yt) max(yt)1,'yticklabel',yl); %limit and label
%to help with the legend modification, keep track of new lines
lbefore = findobj(gcf,'type','line');
ax=gca;
%to put up several tickmarks in the pseudo-legend
%you need one symbol per line
%legend('150 AoC','175 AoC','200 AoC','225 AoC',0);
legend(s(m,:),1);
%make marks in legend for each entry
lafter = findobj(gcf,'type','line');
Inew = setdiff(lafter,lbefore);
for k=1:length(lnew)
ly = get(lnew(k),'ydata');
set(lnew(k),'xdata',.3,'ydata',ly(1));
end
gcf;
%set(gcf,'PaperPosition', [1.5 2 5.5 4]);
set(gca,'position', [0.20 0.12 0.675 0.815])
% A function to obtain model comparison with data plots
% Generating curves and model fits for all data sets
best=[1.01 2.04 3.49;9.214E-02 1.044E-01 1.337E-01;11.015 12.499 15.40];
yi=[ 0.008 -0.026 0.30];
number=3;
s=['d150' ; 'd175'; 'd200' ; 'd225' ; 'd250' ; 'd275' ; 'd300'];
m=7;
for i=m,
a=s(i,:);
load(a);
data=eval(a);
figure(l);
plotdata(data,'ks',l);
hold on;
end
for i=m,
T=125+273+i*25;
a=s(i,:);
load(a);
data=eval(a);
[model]=plotsimr(best(2,:),T,best(3,:),yi,best(1,:),data,number);
plotdata(model,'ro',0);
end
axl=gca;
%set(gca,'FontSize',12,'FontName','Times','XLim', [ 400],'YLim', [-0.020 0.01]);
set(gca,'FontSize',18,'FontName','Helvetica','XLim', [0 400]);
%to help with the legend modification, keep track of new lines
lbefore = findobj(gcf,'type','line');
%to put up several tickmarks in the pseudo-legend
%you need one symbol per line
legend('300 AoC','Model',0);
%make 1 marks in legend for each entry
lafter = findobj(gcf,'type','line');
Inew = setdiff(lafter,lbefore);
for k=1:length(lnew),
ly = get(lnew(k),'ydata');
set(lnew(k),'xdata',.3,'ydata',ly(1,1));
end
for k=length(lnew),
ly=get(lnew(k),'ydata');
set(lnew(k),'xdata',.23:0.07:0.37,'ydata',ones(1,3)*ly(1));
end
% To put a line at [0 0]
xlim=get(axl,'xlim');
l=line(xlim,[0 0] ,'color','k','parent',axl);
% to put in formatted tick labels
yt3 = -0.05:0.05:.30; %ticks
y13 = sprintf('%.2fI ',yt3); %tick label with extra I
yl3(end) = []; %without extra I
set(gca,'ylim', [min(yt3) max(yt3)],'yticklabel',yl3); %limit and label
gcf;
%set(gcf,'PaperPosition', [1.5 2 5.5 4]);
set(gca,'position', [0.20 0.12 0.675 0.8051)
% File plotsimr.m
% A file to generate the model values specifically for the curves
function[model] =plotsimr(K,T,Ea, yi, ni, data, number)
% This is a function for simulating multiple reactions and
% gives the total alpha which make use of a full model using activation
% energy and temperature
% Initialization and data set size determiniation etc.
deltat=7200;
%r=size(data,1);
%N=data(r,1);
% Plot for 400 hours
Nu=200;
alpha(l:Nu,1:number)=0;
dalphadt(l:Nu,l:number)=0;
R=8.314;
duml=0;
dum2=0;
dum3=0;
% Calculating the reaction coeff
94
for m=l:number,
duml=-Ea(m)*1le4;
dum2=R*T;
dum3=exp(duml/dum2);
C(m)=K(m)*lel0*dum3;
end
% Simulating the reactions using a finite difference scheme
for j=l:number,
for i=l:Nu,
if alpha(ij) <= 1 & alpha(ij) >=0
dalphadt(ij)=C(j)*(1-alpha(ij)) ni(j);
alpha(i+lj)=alpha(ij)+dalphadt(ij)*deltat;
if alpha(i+lj) > 1 alpha(i+lj)=l; end
if alpha(i+lj) < 0 alpha(i+lj)=0; end
elseif alpha(ij) < 0
dalphadt(ij)=0;
alpha(i+lj)=0;
elseif alpha(ij) > 1
dalphadt(ij)=0;
alpha(i+lj)=l;
end
t(i)=i*(deltat/3600);
%
t(i)=i*0.5;
end
end
alpha T(1:Nu,1)=O;
% Sum the reactions metrics weighted by their mass fractions
for j=l:number;
alphaT=alpha_T+yi(j)*alpha(1:Nuj);
end
model(Nu,2)=0;
model(1:Nu,1)=[t'];
model(l:Nu,2)= [alpha_T];
APPENDIX B
ISOTHERMAL AGING IN AIR TEST DATA
In all the tables given here, Time is in hours, Sample Mass and Mass
loss are in grams. Normalized Mass Loss is given in the last column.
Table B.1
Data for test at 125 0 C
Mass loss
Sample Mass
Time
0.0000
0.6438
0.0
0.0009
0.6429
2.0
0.0010
0.6428
4.0
0.0009
0.6429
6.0
-0.0003
0.6441
19.0
-0.0005
0.6443
21.0
0.0005
0.6433
23.0
0.0006
0.6432
50.0
0.0005
0.6433
52.0
-0.0001
0.6439
56.0
0.0010
0.6428
74.0
-0.0001
0.6439
76.0
-0.0002
0.6440
79.5
0.0001
0.6437
97.0
-0.0002
0.6440
99.5
-0.0005
0.6443
122.0
0.0000
0.6438
124.0
0.0000
0.6438
127.0
0.0007
0.6431
130.5
0.0002
0.6436
142.0
-0.0002
0.6440
146.0
-0.0011
0.6449
148.0
-0.0007
0.6445
171.0
0.0000
0.6438
191.0
-0.0003
0.6441
194.0
-0.0008
0.6446
214.0
Normalized
0.0000
0.0014
0.0016
0.0014
-0.0005
-0.0008
0.0008
0.0009
0.0008
-0.0002
0.0016
-0.0002
-0.0003
0.0002
-0.0003
-0.0008
0.0000
0.0000
0.0011
0.0003
-0.0003
-0.0017
-0.0011
0.0000
-0.0005
-0.0012
Table B.2
Time
0.0
1.0
26.0
30.5
50.5
54.5
65.5
69.0
73.0
77.0
92.5
96.0
101.0
115.0
119.0
142.0
154.0
Sample Mass
0.7472
0.7458
0.7427
0.7420
0.7430
0.7418
0.7444
0.7430
0.7436
0.7443
0.7439
0.7435
0.7429
0.7437
0.7441
0.7441
0.7440
Data for test at 150°C
Mass Loss
0.0000
0.0014
0.0045
0.0052
0.0042
0.0054
0.0028
0.0042
0.0036
0.0029
0.0033
0.0037
0.0043
0.0035
0.0031
0.0031
0.0032
Normalized
0.0000
0.0019
0.0060
0.0070
0.0056
0.0072
0.0037
0.0056
0.0048
0.0039
0.0044
0.0050
0.0058
0.0047
0.0041
0.0041
0.0043
Table B.3
Sample Mass
Time
0.6604
0.0
0.6590
1.5
0.6585
23.0
0.6650
33.5
0.6642
60.0
0.6677
64.0
0.6653
86.0
0.6674
107.0
0.6662
116.5
0.6679
129.5
0.6685
154.5
0.6685
162.0
0.6666
177.0
0.6679
184.0
0.6679
202.0
0.6674
212.0
0.6701
240.0
0.6694
283.5
0.6707
307.5
0.6708
320.5
0.6678
333.0
0.6709
360.0
0.6712
392.0
0.6713
407.0
0.6718
461.0
0.6711
486.0
0.6714
502.0
0.6719
525.0
0.6723
552.5
0.6723
573.5
0.6717
602.5
Data for test at 175 0 C
Normalized
Mass Loss
0.0000
0.0000
0.0021
0.0014
0.0029
0.0019
-0.0070
-0.0046
-0.0058
-0.0038
-0.0111
-0.0073
-0.0074
-0.0049
-0.0106
-0.0070
-0.0088
-0.0058
-0.0114
-0.0075
-0.0123
-0.0081
-0.0123
-0.0081
-0.0094
-0.0062
-0.0114
-0.0075
-0.0114
-0.0075
-0.0106
-0.0070
-0.0147
-0.0097
-0.0136
-0.0090
-0.0156
-0.0103
-0.0157
-0.0104
-0.0112
-0.0074
-0.0159
-0.0105
-0.0164
-0.0108
-0.0165
-0.0109
-0.0173
-0.0114
-0.0162
-0.0107
-0.0167
-0.0110
-0.0174
-0.0115
-0.0180
-0.0119
-0.0180
-0.0119
-0.0171
-0.0113
Table B.4
Time
0.0
2.0
4.0
6.0
8.0
10.0
21.0
23.0
25.5
29.0
31.0
34.0
45.5
48.0
50.0
57.0
68.5
72.0
76.5
82.0
94.5
96.0
101.5
104.0
120.0
146.0
150.0
152.0
166.0
169.0
172.0
188.0
191.0
193.0
196.5
200.0
202.0
212.0
215.5
220.5
223.0
226.0
240.0
242.0
244.0
249.5
Sample Mass
0.5893
0.5875
0.5889
0.5885
0.5891
0.5887
0.5916
0.5915
0.5915
0.5914
0.5914
0.5921
0.5932
0.5931
0.5936
0.5942
0.5941
0.5947
0.5943
0.5941
0.5959
0.5946
0.5952
0.5955
0.5952
0.5961
0.5969
0.5965
0.5963
0.5964
0.5970
0.5972
0.5975
0.5981
0.5981
0.5969
0.5958
0.5980
0.5961
0.5966
0.5967
0.5964
0.5969
0.5966
0.5977
0.5963
Data for test at 2000 C
Mass Loss
0.0000
0.0018
0.0004
0.0008
0.0002
0.0006
-0.0023
-0.0022
-0.0022
-0.0021
-0.0021
-0.0028
-0.0039
-0.0038
-0.0043
-0.0049
-0.0048
-0.0054
-0.0050
-0.0048
-0.0066
-0.0053
-0.0059
-0.0062
-0.0059
-0.0068
-0.0076
-0.0072
-0.0070
-0.0071
-0.0077
-0.0079
-0.0082
-0.0088
-0.0088
-0.0076
-0.0065
-0.0087
-0.0068
-0.0073
-0.0074
-0.0071
-0.0076
-0.0073
-0.0084
-0.0070
99
Normalized
0.0000
0.0031
0.0007
0.0014
0.0003
0.0010
-0.0039
-0.0037
-0.0037
-0.0036
-0.0036
-0.0048
-0.0066
-0.0064
-0.0073
-0.0083
-0.0081
-0.0092
-0.0085
-0.0081
-0.0112
-0.0090
-0.0100
-0.0105
-0.0100
-0.0115
-0.0129
-0.0122
-0.0119
-0.0120
-0.0131
-0.0134
-0.0139
-0.0149
-0.0149
-0.0129
-0.0110
-0.0148
-0.0115
-0.0124
-0.0126
-0.0120
-0.0129
-0.0124
-0.0143
-0.0119
Table B.4 (contd.)
Time
268.0
289.0
315.0
320.0
333.0
338.0
345.0
Sample Mass
0.5978
0.5968
0.5964
0.5962
0.5973
0.5966
0.5966
Mass Loss
-0.0085
-0.0075
-0.0071
-0.0069
-0.0080
-0.0073
-0.0073
100
Normalized
-0.0144
-0.0127
-0.0120
-0.0117
-0.0136
-0.0124
-0.0124
Table B.5
Time
0.0
2.5
4.0
16.0
18.5
22.0
41.0
44.0
64.5
68.5
95.5
116.5
137.0
141.0
162.5
168.0
188.0
219.5
226.0
251.0
271.5
298.5
320.0
342.0
364.0
Sample Mass
0.6588
0.6598
0.6592
0.6659
0.6658
0.6658
0.6670
0.6669
0.6665
0.6659
0.6650
0.6629
0.6620
0.6622
0.6611
0.6599
0.6590
0.6570
0.6556
0.6546
0.6514
0.6496
0.6482
0.6463
0.6446
Data for test at 225°C
Mass Loss
0.0000
-0.0010
-0.0004
-0.0071
-0.0070
-0.0070
-0.0082
-0.0081
-0.0077
-0.0071
-0.0062
-0.0041
-0.0032
-0.0034
-0.0023
-0.0011
-0.0002
0.0018
0.0032
0.0042
0.0074
0.0092
0.0106
0.0125
0.0142
101
Normalized
0.0000
-0.0015
-0.0006
-0.0108
-0.0106
-0.0106
-0.0124
-0.0123
-0.0117
-0.0108
-0.0094
-0.0062
-0.0049
-0.0052
-0.0035
-0.0017
-0.0003
0.0027
0.0049
0.0064
0.0112
0.0140
0.0161
0.0190
0.0216
Table B.6
Time
0.0
2.0
5.0
8.0
20.5
23.5
27.0
30.0
45.5
48.5
51.0
60.0
69.5
78.5
92.5
98.0
103.0
117.5
121.0
125.0
128.5
140.5
144.0
148.0
152.5
163.5
167.5
171.5
176.5
187.5
193.0
210.0
214.0
218.0
239.0
244.5
271.5
282.5
287.0
306.5
311.5
330.5
337.5
355.5
Sample Mass
0.5639
0.5626
0.5654
0.5636
0.5660
0.5659
0.5659
0.5650
0.5660
0.5629
0.5626
0.5618
0.5558
0.5546
0.5514
0.5491
0.5475
0.5427
0.5434
0.5426
0.5422
0.5406
0.5406
0.5392
0.5380
0.5326
0.5320
0.5308
0.5294
0.5269
0.5260
0.5239
0.5245
0.5235
0.5184
0.5175
0.5146
0.5130
0.5146
0.5118
0.5115
0.5093
0.5077
0.5059
Data for test at 250 0 C
Mass Loss
0.0000
0.0013
-0.0015
0.0003
-0.0021
-0.0020
-0.0020
-0.0011
-0.0021
0.0010
0.0013
0.0021
0.0081
0.0093
0.0125
0.0148
0.0164
0.0212
0.0205
0.0213
0.0217
0.0233
0.0233
0.0247
0.0259
0.0313
0.0319
0.0331
0.0345
0.0370
0.0379
0.0400
0.0394
0.0404
0.0455
0.0464
0.0493
0.0509
0.0493
0.0521
0.0524
0.0546
0.0562
0.0580
102
Normalized
0.0000
0.0023
-0.0027
0.0005
-0.0037
-0.0035
-0.0035
-0.0020
-0.0037
0.0018
0.0023
0.0037
0.0144
0.0165
0.0222
0.0262
0.0291
0.0376
0.0364
0.0378
0.0385
0.0413
0.0413
0.0438
0.0459
0.0555
0.0566
0.0587
0.0612
0.0656
0.0672
0.0709
0.0699
0.0716
0.0807
0.0823
0.0874
0.0903
0.0874
0.0924
0.0929
0.0968
0.0997
0.1029
Table B.6
Time
378.5
409.5
431.5
449.5
473.0
501.0
524.0
541.5
572.0
596.0
622.5
637.0
665.0
688.0
732.0
781.0
806.0
829.0
859.5
878.5
912.5
934.5
949.5
960.0
979.5
1009.0
1028.5
1055.5
1078.0
1103.0
1123.0
1147.0
1172.0
1197.5
1219.0
1247.0
1266.5
1293.0
1316.5
1340.0
1362.5
1394.0
1414.0
1436.5
Sample Mass
0.5046
0.5024
0.4995
0.4995
0.4982
0.4944
0.4940
0.4938
0.4896
0.4898
0.4881
0.4873
0.4861
0.4840
0.4828
0.4812
0.4789
0.4774
0.4774
0.4757
0.4730
0.4726
0.4728
0.4733
0.4724
0.4721
0.4709
0.4682
0.4688
0.4669
0.4668
0.4665
0.4648
0.4633
0.4624
0.4613
0.4608
0.4591
0.4592
0.4586
0.4582
0.4556
0.4545
0.4557
(contd.)
Mass Loss
0.0593
0.0615
0.0644
0.0644
0.0657
0.0695
0.0699
0.0701
0.0743
0.0741
0.0758
0.0766
0.0778
0.0799
0.0811
0.0827
0.0850
0.0865
0.0865
0.0882
0.0909
0.0913
0.0911
0.0906
0.0915
0.0918
0.0930
0.0957
0.0951
0.0970
0.0971
0.0974
0.0991
0.1006
0.1015
0.1026
0.1031
0.1048
0.1047
0.1053
0.1057
0.1083
0.1094
0.1082
103
Normalized
0.1052
0.1091
0.1142
0.1142
0.1165
0.1232
0.1240
0.1243
0.1318
0.1314
0.1344
0.1358
0.1380
0.1417
0.1438
0.1467
0.1507
0.1534
0.1534
0.1564
0.1612
0.1619
0.1616
0.1607
0.1623
0.1628
0.1649
0.1697
0.1686
0.1720
0.1722
0.1727
0.1757
0.1784
0.1800
0.1819
0.1828
0.1858
0.1857
0.1867
0.1874
0.1921
0.1940
0.1919
Table B.7
Time
0.0
2.0
5.0
20.0
23.0
28.0
43.0
48.0
73.0
93.5
103.0
123.0
140.0
145.5
168.0
173.5
192.0
199.0
Sample Mass
0.7449
0.7445
0.7468
0.7299
0.7279
0.7223
0.7107
0.7071
0.6923
0.6851
0.6807
0.6740
0.6682
0.6643
0.6598
0.6593
0.6553
0.6518
Data for test at 2750 C
Mass Loss
0.0000
0.0004
-0.0019
0.0150
0.0170
0.0226
0.0342
0.0378
0.0526
0.0598
0.0642
0.0709
0.0767
0.0806
0.0851
0.0856
0.0896
0.0931
104
Normalized
0.0000
0.0004
-0.0019
0.0150
0.0170
0.0226
0.0342
0.0378
0.0526
0.0598
0.0642
0.0709
0.0767
0.0806
0.0851
0.0856
0.0896
0.0931
Table B.8
Time
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
11.0
12.0
13.0
23.0
24.0
25.0
26.0
50.0
74.0
91.0
95.0
98.0
104.0
116.0
120.0
124.0
128.0
141.0
143.0
146.0
150.0
164.0
168.0
172.0
188.0
Sample Mass
0.6881
0.6901
0.6912
0.6901
0.6853
0.6845
0.6836
0.6832
0.6809
0.6796
0.6782
0.6771
0.6756
0.6746
0.6612
0.6599
0.6592
0.6586
0.6346
0.6196
0.6136
0.6106
0.6116
0.6071
0.6021
0.6011
0.6000
0.5976
0.5956
0.5946
0.5926
0.5906
0.5856
0.5849
0.5841
0.5806
Data for test at 3000 C
Mass Loss
0.0000
-0.0020
-0.0031
-0.0020
0.0028
0.0036
0.0045
0.0049
0.0072
0.0085
0.0099
0.0110
0.0125
0.0135
0.0269
0.0282
0.0289
0.0295
0.0535
0.0685
0.0745
0.0775
0.0765
0.0810
0.0860
0.0870
0.0881
0.0905
0.0925
0.0935
0.0955
0.0975
0.1025
0.1032
0.1040
0.1075
105
Normalized
0.0000
-0.0029
-0.0045
-0.0029
0.0041
0.0052
0.0065
0.0071
0.0105
0.0124
0.0144
0.0160
0.0182
0.0196
0.0391
0.0410
0.0420
0.0429
0.0778
0.0995
0.1083
0.1126
0.1112
0.1177
0.1250
0.1264
0.1280
0.1315
0.1344
0.1359
0.1388
0.1417
0.1490
0.1500
0.1511
0.1562